A Scalable Deep Learning Framework for Wave-Based Inverse Problems
Production-ready • Multi-GPU DDP • Memory-Efficient • Plug-and-Play
Getting Started • Documentation • Examples • Discussions • Citation
Plug in your model, load your data, and let WaveDL do the heavy lifting 💪
💡 What is WaveDL?
WaveDL is a deep learning framework built for wave-based inverse problems — from ultrasonic NDE and geophysics to biomedical tissue characterization. It provides a robust, scalable training pipeline for mapping multi-dimensional data (1D/2D/3D) to physical quantities or dense 2D property fields.
Input: Waveforms, spectrograms, B-scans, dispersion curves, ...
↓
Output: Material properties, defect dimensions, elasticity/velocity maps, ...
The framework handles the engineering challenges of large-scale deep learning — big datasets, distributed training, and HPC deployment — so you can focus on the science, not the infrastructure.
Built for researchers who need:
- 📊 Vector and dense 2D regression with reproducibility and fair benchmarking
- 🚀 Seamless multi-GPU training on HPC clusters
- 💾 Memory-efficient handling of large-scale datasets
- 🔧 Easy integration of custom model architectures
✨ Features
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⚡ Dataset Caching Prepare data for repeated training:
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🧠 Models? We've Got Options 20+ architectures (70+ variants), ready to go:
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🛡️ Distributed Training Coordinate training across ranks:
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🔬 Physics-Constrained Training Make your model respect the laws:
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🖥️ HPC-Native Design Built for high-performance clusters:
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🔄 Training Recovery Resume interrupted experiments:
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🎛️ Flexible & Reproducible Training Fully configurable via CLI flags or YAML:
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📦 ONNX Export Deploy models anywhere:
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🚀 Getting Started
Installation
From PyPI (recommended for all users)
pip install --upgrade wavedl
This installs the training, inference, HPO, and ONNX export dependencies.
The unreleased source requires Python 3.11+, PyTorch 2.13+, torchvision 0.28+,
and ONNX 1.22+. Install a compatible PyTorch/torchvision pair for your CPU or
CUDA/ROCm platform in a dedicated environment. Changes under [Unreleased]
are available from source until the next package release.
See security and deployment boundaries for vulnerability reporting procedures, safe deserialization practices, and secure data handling guidelines.
From Source (for development)
git clone https://github.com/ductho-le/WaveDL.git
cd WaveDL
pip install -e ".[dev]"
Quick Start
Training
# Basic training (auto-detects GPUs and environment)
wavedl-train --model <model_name> --data_path <train_data> --output_dir <output_folder>
# Detailed configuration
wavedl-train --model <model_name> --data_path <train_data> --batch_size <number> \
--lr <number> --epochs <number> --patience <number> --compile --output_dir <output_folder>
# Multi-GPU is automatic (uses all available GPUs)
# Override with --num_gpus if needed
wavedl-train --model cnn --data_path train.npz --num_gpus 4 --output_dir results
# Resume training (automatic - just re-run with same output_dir)
wavedl-train --model <model_name> --data_path <train_data> --output_dir <output_folder>
# Force fresh start (archives prior training artifacts under previous_runs/)
wavedl-train --model <model_name> --data_path <train_data> --output_dir <output_folder> --fresh
# List available models
wavedl-train --list_models
Advanced: Direct Accelerate Launch
For fine-grained control over distributed training, you can use accelerate launch directly:
# Custom accelerate configuration
accelerate launch -m wavedl.train --model <model_name> --data_path <train_data> --output_dir <output_folder>
# Multi-node training
accelerate launch --num_machines 2 --main_process_ip <ip> -m wavedl.train --model cnn --data_path train.npz
Testing & Inference
# Basic inference
wavedl-test --checkpoint <checkpoint_folder> --data_path <test_data>
# With visualization, prediction export, and multiple plot formats
wavedl-test --checkpoint <checkpoint_folder> --data_path <test_data> \
--plot --plot_format png pdf --save_predictions --output_dir <output_folder>
# With custom parameter names
wavedl-test --checkpoint <checkpoint_folder> --data_path <test_data> \
--param_names '$p_1$' '$p_2$' '$p_3$' --plot
# Export model to ONNX for deployment (LabVIEW, MATLAB, C++, etc.)
wavedl-test --checkpoint <checkpoint_folder> --data_path <test_data> \
--export onnx --export_path <output_file.onnx>
# For 3D volumes with small depth (e.g., 8×128×128), override auto-detection
wavedl-test --checkpoint <checkpoint_folder> --data_path <test_data> \
--input_channels 1
Output:
- Console: R², Pearson correlation, and MAE per parameter/channel; dense fields also report relative L2 error
- Predictions (with
--save_predictions): vector outputs use CSV; dense fields use compressedpredictions.npzwithtarget,prediction,error, andchannel_namesarrays (or onlypredictionandchannel_nameswhen targets are absent) - Plots (with
--plot): vectors produce 10 publication-quality diagnostic plots; dense fields with ground truth produce target, prediction, and error maps - Format (with
--plot_format): Supported formats:png(default),pdfandsvg(vector graphics),eps(LaTeX),tiff,jpg,ps
For dense fields, R² and Pearson correlation are computed independently per property channel over all sample-pixel values and then averaged; MAE/RMSE also aggregate spatial values, while relative L2 error averages sample/channel field norms. Field plots are intentionally limited to the first three samples and six channels to keep result directories manageable.
Dense 2D Field Regression
Use --model unet_field for supervised, pixel-wise prediction of an elasticity, stiffness, velocity, density, or similar 2D property map. This model is field-only; continue using unet_regression or another vector architecture for (N, T) targets. The built-in field model follows WaveDL's existing single-channel input convention: store each input as (H_in, W_in), and the data loader adds the channel axis internally.
Accepted target layouts are:
| Stored target layout | Meaning | Model layout |
|---|---|---|
(N, H_out, W_out) |
One scalar field per sample | (N, 1, H_out, W_out) |
(N, C, H_out, W_out) |
C property fields per sample |
unchanged |
Targets must be channels-first; channels-last arrays such as (N, H, W, C) are not guessed and should be transposed before saving. The 2D input and output grid resolutions are independent, so (H_in, W_in) may differ from (H_out, W_out), but their spatial rank must match. unet_field infers the target grid during training and interpolates its dense head to that size. Each output channel is standardized independently using statistics over the training samples and both spatial axes, rather than fitting a separate scaler at every pixel.
Dense caches record their normalization version and rebuild automatically after
normalization changes. Checkpoints from the earlier experimental dense scaler
require retraining with --fresh or a new output directory. Vector checkpoints
retain their target normalization. Legacy Mamba/Vim weights are an exception:
the corrected selective scan changes predictions, so unversioned scan weights
are rejected. Use the original WaveDL version for legacy inference/resume, or
retrain with --fresh. New checkpoints store the scan version in their weights.
WaveNet retains the published optimizer parameter layout for resume compatibility.
Resuming also verifies that the current training
split has the same target normalization as the saved checkpoint.
This small synthetic example exercises different input/output grid sizes:
import numpy as np
rng = np.random.default_rng(7)
wave_images = rng.normal(size=(80, 64, 96)).astype(np.float32)
property_maps = wave_images[:, ::2, ::2] # (N, H_out, W_out) = (80, 32, 48)
np.savez(
"field_data.npz",
input_train=wave_images[:64],
output_train=property_maps[:64],
input_test=wave_images[64:],
output_test=property_maps[64:],
)
wavedl-train --model unet_field --data_path field_data.npz --batch_size 4 --epochs 5 \
--output_dir field_run
wavedl-test --checkpoint field_run/best_checkpoint --data_path field_data.npz \
--param_names property --save_predictions --plot --output_dir field_results
For multiple output properties, stack maps on axis 1 to create (N, C, H_out, W_out) targets. The channel count is detected automatically; no output-grid CLI flag is required.
Dense decoders and target maps use substantially more GPU memory and disk than
vector regression. Start with a small batch size (for example, 1–8). Training
also creates target_data_cache.dat in the output directory with size roughly
N × C × H_out × W_out × 4 bytes, so place the output directory on scratch
storage with adequate quota for large FWI or elastography datasets.
Adding Custom Models
Creating Your Own Architecture
Requirements (for a vector-output model):
- Inherit from
BaseModel - Accept
in_shape,out_sizein__init__ - Return a tensor of shape
(batch, out_size)fromforward()
Step 1: Create my_model.py
import torch.nn as nn
import torch.nn.functional as F
from wavedl.models import BaseModel, register_model
@register_model("my_model") # This name is used with --model flag
class MyModel(BaseModel):
def __init__(self, in_shape, out_size, **kwargs):
# in_shape: spatial dimensions, e.g., (128,) or (64, 64) or (32, 32, 32)
# out_size: number of parameters to predict (auto-detected from data)
super().__init__(in_shape, out_size)
# Define your layers (this is just an example for 2D)
self.conv1 = nn.Conv2d(1, 64, 3, padding=1) # Input always has 1 channel
self.conv2 = nn.Conv2d(64, 128, 3, padding=1)
self.fc = nn.Linear(128, out_size)
def forward(self, x):
# Input x has shape: (batch, 1, *in_shape)
x = F.relu(self.conv1(x))
x = F.relu(self.conv2(x))
x = x.mean(dim=[-2, -1]) # Global average pooling
return self.fc(x) # Output shape: (batch, out_size)
Step 2: Train
wavedl-train --import my_model.py --model my_model --data_path train.npz
WaveDL handles everything else: training loop, logging, checkpoints, multi-GPU, early stopping, etc.
For a custom dense 2D model, also accept the inferred out_shape=(C, H_out, W_out), set supports_spatial_output = True (and requires_spatial_output = True if it cannot emit vectors), and return exactly (batch, C, H_out, W_out).
📁 Project Structure
WaveDL/
├── src/
│ └── wavedl/ # Main package (namespaced)
│ ├── __init__.py # Package init with __version__
│ ├── train.py # Training script
│ ├── test.py # Testing & inference script
│ ├── hpo.py # Hyperparameter optimization
│ ├── launcher.py # Training launcher (wavedl-train)
│ │
│ ├── models/ # Model Zoo (20+ architectures, 70+ variants)
│ │ ├── registry.py # Model factory (@register_model)
│ │ ├── base.py # Abstract base class
│ │ └── ... # See "Available Models" section
│ │
│ └── utils/ # Utilities
│ ├── data.py # Memory-mapped data pipeline
│ ├── metrics.py # R², Pearson, visualization
│ ├── constraints.py # Physical constraints for training
│ ├── distributed.py # DDP synchronization
│ ├── losses.py # Loss function factory
│ ├── optimizers.py # Optimizer factory
│ ├── schedulers.py # LR scheduler factory
│ └── config.py # YAML configuration support
│
├── configs/ # YAML config templates
├── examples/ # Ready-to-run examples
├── notebooks/ # Jupyter notebooks
├── unit_tests/ # Pytest test suite
│
├── pyproject.toml # Package config, dependencies
├── CHANGELOG.md # Version history
└── CITATION.cff # Citation metadata
⚙️ Configuration
Available Models — 20+ architectures (70+ variants)
Output support
| Output type | Built-in models | Stored target | Model output |
|---|---|---|---|
| Vector regression | Every model except unet_field |
(N,) or (N, T) |
(N, T) |
| Dense 2D field | unet_field |
(N, H_out, W_out) or (N, C, H_out, W_out) |
(N, C, H_out, W_out) |
The dimensionality column below describes the input. A model accepting 2D input does not automatically support dense output; look at the output-support table above when selecting a model.
| Model | Backbone Params | Input Dim |
|---|---|---|
| ── Classic CNNs ── | ||
| CNN — Convolutional Neural Network | ||
cnn |
1.6M | 1D/2D/3D |
| ResNet — Residual Network | ||
resnet18 |
11.2M | 1D/2D/3D |
resnet34 |
21.3M | 1D/2D/3D |
resnet50 |
23.5M | 1D/2D/3D |
resnet18_pretrained ⭐ |
11.2M | 2D |
resnet50_pretrained ⭐ |
23.5M | 2D |
| DenseNet — Densely Connected Network | ||
densenet121 |
7.0M | 1D/2D/3D |
densenet169 |
12.5M | 1D/2D/3D |
densenet121_pretrained ⭐ |
7.0M | 2D |
| ── Efficient/Mobile CNNs ── | ||
| MobileNetV3 — Mobile Neural Network V3 | ||
mobilenet_v3_small ⭐ |
0.9M | 2D |
mobilenet_v3_large ⭐ |
3.0M | 2D |
| EfficientNet — Efficient Neural Network | ||
efficientnet_b0 ⭐ |
5.3M | 2D |
efficientnet_b2 ⭐ |
9.1M | 2D |
efficientnet_b4 ⭐ |
19M | 2D |
efficientnet_b7 ⭐ |
66M | 2D |
| EfficientNetV2 — Efficient Neural Network V2 | ||
efficientnet_v2_s ⭐ |
20.2M | 2D |
efficientnet_v2_m ⭐ |
52.9M | 2D |
efficientnet_v2_l ⭐ |
117.2M | 2D |
| RegNet — Regularized Network | ||
regnet_y_400mf ⭐ |
3.9M | 2D |
regnet_y_800mf ⭐ |
5.7M | 2D |
regnet_y_1_6gf ⭐ |
10.3M | 2D |
regnet_y_3_2gf ⭐ |
17.9M | 2D |
regnet_y_8gf ⭐ |
37.4M | 2D |
| ── Modern CNNs ── | ||
| ConvNeXt — Convolutional Next | ||
convnext_tiny |
27.8M | 1D/2D/3D |
convnext_small |
49.5M | 1D/2D/3D |
convnext_base |
87.6M | 1D/2D/3D |
convnext_tiny_pretrained ⭐ |
27.8M | 2D |
| ConvNeXt V2 — ConvNeXt with GRN | ||
convnext_v2_tiny |
27.9M | 1D/2D/3D |
convnext_v2_small |
49.6M | 1D/2D/3D |
convnext_v2_base |
87.7M | 1D/2D/3D |
convnext_v2_tiny_pretrained ⭐ |
27.9M | 2D |
| UniRepLKNet — Large-Kernel ConvNet | ||
unireplknet_tiny |
30.8M | 1D/2D/3D |
unireplknet_small |
56.0M | 1D/2D/3D |
unireplknet_base |
97.6M | 1D/2D/3D |
| ── Vision Transformers ── | ||
| ViT — Vision Transformer | ||
vit_tiny |
5.4M | 1D/2D |
vit_small |
21.4M | 1D/2D |
vit_base |
85.3M | 1D/2D |
| Swin — Shifted Window Transformer | ||
swin_t ⭐ |
27.5M | 2D |
swin_s ⭐ |
48.8M | 2D |
swin_b ⭐ |
86.7M | 2D |
| MaxViT — Multi-Axis ViT | ||
maxvit_tiny ⭐ |
30.1M | 2D |
maxvit_small ⭐ |
67.6M | 2D |
maxvit_base ⭐ |
119.1M | 2D |
| ── Hybrid CNN-Transformer ── | ||
| FastViT — Fast Hybrid CNN-ViT | ||
fastvit_t8 ⭐ |
4.0M | 2D |
fastvit_t12 ⭐ |
6.8M | 2D |
fastvit_s12 ⭐ |
8.8M | 2D |
fastvit_sa12 ⭐ |
10.9M | 2D |
| CAFormer — MetaFormer with Attention | ||
caformer_s18 ⭐ |
26.3M | 2D |
caformer_s36 ⭐ |
39.2M | 2D |
caformer_m36 ⭐ |
56.9M | 2D |
poolformer_s12 ⭐ |
11.9M | 2D |
| EfficientViT — Memory-Efficient ViT | ||
efficientvit_m1 ⭐ |
2.6M | 2D |
efficientvit_b1 ⭐ |
7.5M | 2D |
efficientvit_b2 ⭐ |
21.8M | 2D |
efficientvit_l2 ⭐ |
60.5M | 2D |
| ── State Space Models ── | ||
| Mamba — State Space Model | ||
mamba_1d |
3.4M | 1D |
| S4D — Diagonal Structured State Space | ||
s4d_small |
0.8M | 1D |
s4d |
3.2M | 1D |
s4d_large |
11M | 1D |
| Vision Mamba (ViM) — 2D Mamba | ||
vim_tiny |
6.6M | 2D |
vim_small |
51.1M | 2D |
vim_base |
201.4M | 2D |
| ── Specialized Architectures ── | ||
| TCN — Temporal Convolutional Network | ||
tcn_small |
0.9M | 1D |
tcn |
6.9M | 1D |
tcn_large |
10.0M | 1D |
| WaveNet — Gated Dilated Conv Network | ||
wavenet_small |
1.0M | 1D |
wavenet |
4.0M | 1D |
wavenet_large |
15M | 1D |
| ResNet3D — 3D Residual Network | ||
resnet3d_18 |
33.2M | 3D |
mc3_18 — Mixed Convolution 3D |
11.5M | 3D |
| U-Net — U-shaped Network | ||
unet_regression |
31.0M | 1D/2D/3D |
unet_field 🗺️ |
~31.0M | 2D |
⭐ = Pretrained on ImageNet (recommended for smaller datasets). Weights are downloaded automatically on first use.
🗺️ = Dense 2D field output. Unmarked models produce regression vectors.
- Cache location:
~/.cache/torch/hub/checkpoints/(or./.torch_cache/on HPC if home is not writable) - Use pretrained weights: Pass
--pretrained(default: train from scratch). Only effective for*_pretrainedmodel variants marked with ⭐ above.
💡 HPC Users: If compute nodes block internet, pre-download weights on the login node:
# Run once on login node (with internet) — downloads ALL pretrained weights
# Uses download-only approach (no model instantiation) to avoid CPU time limits
python -c "
import os, torch, warnings
warnings.filterwarnings('ignore', category=UserWarning, module='pydantic')
os.environ['TORCH_HOME'] = '.torch_cache' # Match WaveDL's HPC cache location
os.environ['HF_HOME'] = '.hf_cache' # Match WaveDL's HPC cache for timm models
from torchvision import models as m
from torchvision.models import video as v
# === TorchVision + Video Models — download only, no model instantiation ===
urls = [
('ResNet18', m.ResNet18_Weights.IMAGENET1K_V1.url),
('ResNet50', m.ResNet50_Weights.IMAGENET1K_V1.url),
('EfficientNet_B0', m.EfficientNet_B0_Weights.IMAGENET1K_V1.url),
('EfficientNet_B2', m.EfficientNet_B2_Weights.IMAGENET1K_V1.url),
('EfficientNet_B4', m.EfficientNet_B4_Weights.IMAGENET1K_V1.url),
('EfficientNet_B7', m.EfficientNet_B7_Weights.IMAGENET1K_V1.url),
('EfficientNetV2_S', m.EfficientNet_V2_S_Weights.IMAGENET1K_V1.url),
('EfficientNetV2_M', m.EfficientNet_V2_M_Weights.IMAGENET1K_V1.url),
('EfficientNetV2_L', m.EfficientNet_V2_L_Weights.IMAGENET1K_V1.url),
('MobileNetV3_S', m.MobileNet_V3_Small_Weights.IMAGENET1K_V1.url),
('MobileNetV3_L', m.MobileNet_V3_Large_Weights.IMAGENET1K_V1.url),
('RegNet_Y_400MF', m.RegNet_Y_400MF_Weights.IMAGENET1K_V1.url),
('RegNet_Y_800MF', m.RegNet_Y_800MF_Weights.IMAGENET1K_V1.url),
('RegNet_Y_1_6GF', m.RegNet_Y_1_6GF_Weights.IMAGENET1K_V1.url),
('RegNet_Y_3_2GF', m.RegNet_Y_3_2GF_Weights.IMAGENET1K_V1.url),
('RegNet_Y_8GF', m.RegNet_Y_8GF_Weights.IMAGENET1K_V1.url),
('Swin_T', m.Swin_T_Weights.IMAGENET1K_V1.url),
('Swin_S', m.Swin_S_Weights.IMAGENET1K_V1.url),
('Swin_B', m.Swin_B_Weights.IMAGENET1K_V1.url),
('ConvNeXt_Tiny', m.ConvNeXt_Tiny_Weights.IMAGENET1K_V1.url),
('DenseNet121', m.DenseNet121_Weights.IMAGENET1K_V1.url),
('R3D_18', v.R3D_18_Weights.KINETICS400_V1.url),
('MC3_18', v.MC3_18_Weights.KINETICS400_V1.url),
]
cache = os.path.join(os.environ['TORCH_HOME'], 'hub', 'checkpoints')
os.makedirs(cache, exist_ok=True)
for name, url in urls:
torch.hub.download_url_to_file(url, os.path.join(cache, os.path.basename(url)))
print(f' ✓ {name}')
# === Timm Models — download only via HuggingFace Hub ===
import timm
from huggingface_hub import hf_hub_download
timm_models = [
'maxvit_tiny_tf_224', 'maxvit_small_tf_224', 'maxvit_base_tf_224',
'fastvit_t8', 'fastvit_t12', 'fastvit_s12', 'fastvit_sa12',
'caformer_s18', 'caformer_s36', 'caformer_m36', 'poolformer_s12',
'convnextv2_tiny',
'efficientvit_m1', 'efficientvit_b1', 'efficientvit_b2', 'efficientvit_l2',
]
for name in timm_models:
cfg = timm.get_pretrained_cfg(name)
if cfg.hf_hub_id:
hf_hub_download(cfg.hf_hub_id, 'model.safetensors')
elif cfg.url:
torch.hub.download_url_to_file(cfg.url, os.path.join(cache, os.path.basename(cfg.url)))
print(f' ✓ {name}')
print(f'\n✓ All {len(urls) + len(timm_models)} pretrained weight files cached!')
"
Training Parameters
| Argument | Default | Description |
|---|---|---|
--model |
cnn |
Model architecture |
--import |
- | Python file(s) to import for custom models (supports multiple) |
--batch_size |
128 |
Per-GPU batch size |
--lr |
1e-3 |
Learning rate |
--epochs |
1000 |
Maximum epochs |
--patience |
20 |
Early stopping patience |
--weight_decay |
1e-4 |
AdamW regularization |
--grad_clip |
1.0 |
Gradient clipping |
--grad_accum_steps |
1 |
Gradient accumulation steps (simulate larger batch sizes) |
Data & I/O
| Argument | Default | Description |
|---|---|---|
--data_path |
train_data.npz |
Dataset path |
--workers |
-1 |
DataLoader workers per GPU (-1=auto-detect) |
--seed |
2025 |
Random seed |
--output_dir |
. |
Output directory for checkpoints |
--selection_metric |
loss |
Select checkpoints by configured loss or normalized mse; CV supports loss |
--allow_pickle |
False |
Opt in to loading trusted legacy NPZ object arrays |
--resume |
None |
Checkpoint to resume (auto-detected if not set) |
--save_every |
50 |
Checkpoint frequency |
--fresh |
False |
Archive previous training artifacts and start fresh |
--single_channel |
False |
Confirm data is single-channel (for shallow 3D volumes like (8, 128, 128)) |
Performance
| Argument | Default | Description |
|---|---|---|
--compile |
False |
Enable torch.compile (recommended for long runs) |
--precision |
bf16 |
Mixed precision mode (bf16, fp16, no) |
--workers |
-1 |
DataLoader workers per GPU (-1=auto, up to 16) |
--wandb |
False |
Enable W&B logging |
--wandb_watch |
False |
Enable W&B gradient watching (adds overhead) |
--project_name |
DL-Training |
W&B project name |
--run_name |
None |
W&B run name (auto-generated if not set) |
Automatic GPU Optimizations:
WaveDL automatically enables performance optimizations for modern GPUs:
| Optimization | Effect | GPU Support |
|---|---|---|
| TF32 precision | ~2x speedup for float32 matmul | A100, H100 (Ampere+) |
| cuDNN benchmark | Auto-tuned convolutions | All NVIDIA GPUs |
| Worker scaling | Up to 16 workers per GPU | All systems |
HPC Best Practices:
- Stage data to
$SLURM_TMPDIR(local NVMe) for maximum I/O throughput - Use
--compilefor training runs > 50 epochs - Increase
--workersmanually if auto-detection is suboptimal
Distributed Training Arguments
| Argument | Default | Description |
|---|---|---|
--num_gpus |
Auto-detected | Number of GPUs to use. By default, automatically detected via nvidia-smi. Set explicitly to override |
--num_machines |
1 |
Number of machines in distributed setup |
--mixed_precision |
bf16 |
Precision mode: bf16, fp16, or no |
--dynamo_backend |
no |
PyTorch Dynamo backend |
Environment Variables (for logging):
| Variable | Default | Description |
|---|---|---|
WANDB_MODE |
offline |
WandB mode: offline or online |
Loss Functions
| Loss | Flag | Best For | Notes |
|---|---|---|---|
mse |
--loss mse |
Default, smooth gradients | Standard Mean Squared Error |
mae |
--loss mae |
Outlier-robust, linear penalty | Mean Absolute Error (L1) |
huber |
--loss huber --huber_delta 1.0 |
Best of MSE + MAE | Robust, smooth transition |
smooth_l1 |
--loss smooth_l1 |
Similar to Huber | PyTorch native implementation |
log_cosh |
--loss log_cosh |
Smooth approximation to MAE | Differentiable everywhere |
weighted_mse |
--loss weighted_mse --loss_weights "2.0,1.0,1.0" |
Prioritize specific targets/properties | Per-vector-target or per-field-channel weighting |
Example:
# Use Huber loss for noisy NDE data
wavedl-train --model cnn --loss huber --huber_delta 0.5
# Weighted MSE: prioritize thickness (first target)
wavedl-train --model cnn --loss weighted_mse --loss_weights "2.0,1.0,1.0"
# Dense maps: weight the first property channel twice as strongly
wavedl-train --model unet_field --loss weighted_mse --loss_weights "2.0,1.0" \
--data_path field_data.npz --batch_size 4
Optimizers
| Optimizer | Flag | Best For | Key Parameters |
|---|---|---|---|
adamw |
--optimizer adamw |
Default, most cases | --betas "0.9,0.999" |
adam |
--optimizer adam |
Legacy compatibility | --betas "0.9,0.999" |
sgd |
--optimizer sgd |
Better generalization | --momentum 0.9 --nesterov |
nadam |
--optimizer nadam |
Adam + Nesterov | Faster convergence |
radam |
--optimizer radam |
Variance-adaptive | More stable training |
rmsprop |
--optimizer rmsprop |
RNN/LSTM models | --momentum 0.9 |
Example:
# SGD with Nesterov momentum (often better generalization)
wavedl-train --model cnn --optimizer sgd --lr 0.01 --momentum 0.9 --nesterov
# RAdam for more stable training
wavedl-train --model cnn --optimizer radam --lr 1e-3
Learning Rate Schedulers
| Scheduler | Flag | Best For | Key Parameters |
|---|---|---|---|
plateau |
--scheduler plateau |
Default, adaptive | --scheduler_patience 10 --scheduler_factor 0.5 |
cosine |
--scheduler cosine |
Long training, smooth decay | --min_lr 1e-6 |
cosine_restarts |
--scheduler cosine_restarts |
Escape local minima | Warm restarts |
onecycle |
--scheduler onecycle |
Fast convergence | Super-convergence |
step |
--scheduler step |
Simple decay | --step_size 30 --scheduler_factor 0.1 |
multistep |
--scheduler multistep |
Custom milestones | --milestones "30,60,90" |
exponential |
--scheduler exponential |
Continuous decay | --scheduler_factor 0.95 |
linear_warmup |
--scheduler linear_warmup |
Warmup phase | --warmup_epochs 5 |
Example:
# Cosine annealing for 1000 epochs
wavedl-train --model cnn --scheduler cosine --epochs 1000 --min_lr 1e-7
# OneCycleLR for super-convergence
wavedl-train --model cnn --scheduler onecycle --lr 1e-2 --epochs 50
# MultiStep with custom milestones
wavedl-train --model cnn --scheduler multistep --milestones "100,200,300"
Cross-Validation
For robust model evaluation, simply add the --cv flag:
# 5-fold cross-validation
wavedl-train --model cnn --cv 5 --data_path train_data.npz
# Dense 2D field cross-validation (non-stratified)
wavedl-train --model unet_field --cv 5 --data_path field_data.npz \
--batch_size 4
# Stratified CV for unbalanced vector targets
wavedl-train --model cnn --cv 5 --cv_stratify --loss huber --epochs 100
# Full configuration
wavedl-train --model cnn --cv 5 --cv_stratify \
--loss huber --optimizer adamw --scheduler cosine \
--output_dir ./cv_results
| Argument | Default | Description |
|---|---|---|
--cv |
0 |
Number of CV folds (0=disabled, normal training) |
--cv_stratify |
False |
Bin vector targets for stratified splitting; unsupported for dense fields |
--cv_bins |
10 |
Number of bins for stratified CV |
Output:
cv_summary.json: Aggregated metrics (mean ± std)cv_results.csv: Per-fold detailed resultsfold_*/: Individual fold models and scalers
Dense field CV can require substantial host memory because folds are currently
materialized in memory. Do not combine it with --cv_stratify; use smaller
datasets/batches or run separate held-out experiments for very large field maps.
CV preserves custom loss weights, Huber delta, and pretrained initialization.
Physical constraints and gradient accumulation require standard training; CV
rejects these options instead of silently ignoring them. CV runs in one process
and currently selects folds using the configured loss (--selection_metric loss).
Configuration Files (YAML)
Use YAML files for reproducible experiments. CLI arguments can override any config value.
# Use a config file
wavedl-train --config configs/config.yaml --data_path train.npz
# Override specific values from config
wavedl-train --config configs/config.yaml --lr 5e-4 --epochs 500
Example config (configs/config.yaml):
# Model & Training
model: cnn
batch_size: 128
lr: 0.001
epochs: 1000
patience: 20
# Loss, Optimizer, Scheduler
loss: mse
optimizer: adamw
scheduler: plateau
# Cross-Validation (0 = disabled)
cv: 0
# Performance
precision: bf16
compile: false
seed: 2025
See
configs/config.yamlfor the complete template with all available options documented.
Physical Constraints — Enforce Physics During Training
Add penalty terms to the loss function to enforce physical laws:
Total Loss = Data Loss + weight × penalty(violation)
Expression Constraints
# Positivity
--constraint "y0 > 0"
# Bounds
--constraint "y0 >= 0" "y0 <= 1"
# Equations (penalize deviations from zero)
--constraint "y2 - y0 * y1"
# Input-dependent constraints
--constraint "y0 - 2*x[0]"
# Multiple constraints with different weights
--constraint "y0 > 0" "y1 - y2" --constraint_weight 0.1 1.0
Custom Python Constraints
For complex physics (matrix operations, implicit equations):
# my_constraint.py
import torch
def constraint(pred, inputs=None):
"""
Args:
pred: (batch, num_outputs) vectors or (batch, C, H, W) fields
inputs: (batch, features) or (batch, C, H, W) or (batch, C, D, H, W)
Returns:
Violation tensor; WaveDL reduces all returned values to one penalty.
"""
# For vectors, y0/y1/y2 are (batch,). For dense outputs they are
# (batch, H, W), so this same expression applies at every pixel.
y0, y1, y2 = pred[:, 0], pred[:, 1], pred[:, 2]
# Inputs — Tabular: (batch, features)
# x0 = inputs[:, 0] # Feature 0
# x_sum = inputs.sum(dim=1) # Sum all features
# Inputs — Images: (batch, C, H, W)
# pixel = inputs[:, 0, 3, 5] # Pixel at (3,5), channel 0
# img_mean = inputs.mean(dim=(1,2,3)) # Mean over C,H,W
# Inputs — 3D Volumes: (batch, C, D, H, W)
# voxel = inputs[:, 0, 2, 3, 5] # Voxel at (2,3,5), channel 0
# Example constraints:
# return y2 - y0 * y1 # Wave equation
# return y0 - 2 * inputs[:, 0] # Output = 2×input
# return inputs[:, 0, 3, 5] * y0 + inputs[:, 0, 6, 7] * y1 # Mixed
return y0 - y1 * y2
--constraint_file my_constraint.py --constraint_weight 1.0
Reference
| Argument | Default | Description |
|---|---|---|
--constraint |
— | Expression(s): "y0 > 0", "y0 - y1*y2" |
--constraint_file |
— | Python file with constraint(pred, inputs) |
--constraint_weight |
0.1 |
Penalty weight(s) |
--constraint_reduction |
mse |
mse (squared) or mae (linear) |
Expression Syntax
| Variable | Meaning |
|---|---|
y0, y1, ... |
Vector outputs (B,) or dense property channels (B,H,W) |
x[0], x[1], ... |
Input values (1D tabular) |
x[i,j], x[i,j,k] |
Input values (2D/3D: images, volumes) |
x_mean, x_sum, x_max, x_min, x_std |
Input aggregates |
Operators: +, -, *, /, **, >, <, >=, <=, ==
Functions: sin, cos, exp, log, sqrt, sigmoid, softplus, tanh, relu, abs
Hyperparameter Search (HPO)
Automatically find the best training configuration using Optuna.
Run HPO:
# Basic HPO (50 trials, auto-detects GPUs)
wavedl-hpo --data_path train.npz --n_trials 50
# Quick search (minimal search space, fastest)
wavedl-hpo --data_path train.npz --n_trials 30 --quick
# Medium search (balanced between quick and full)
wavedl-hpo --data_path train.npz --n_trials 50 --medium
# Full search with specific models
wavedl-hpo --data_path train.npz --n_trials 100 --models cnn resnet18 efficientnet_b0
# Dense field search (auto-selects unet_field and small batch candidates)
wavedl-hpo --data_path field_data.npz --n_trials 30
# In-process mode (enables pruning, faster, single-GPU)
wavedl-hpo --data_path train.npz --n_trials 50 --inprocess
HPO inspects the target shape before creating a study. Vector data uses the
standard CNN/ResNet model presets and batch candidates 16/32/64/128. Dense data
uses unet_field and batch candidates 1/2/4/8. Explicit --models values are
validated against the target contract before any trials launch; use
--batch_sizes to override the memory-conscious dense defaults.
HPO compares trials using the same normalized validation MSE, even when their training losses differ. It seeds the sampler and records a study signature covering the dataset, search settings, and objective. Use a new study name when those settings change or when migrating a legacy study without this signature; mixing incompatible trials is rejected. Parallel trials lease distinct visible GPUs.
Train with best parameters
After HPO completes, it prints the optimal command:
wavedl-train --data_path train.npz --model cnn --lr 3.2e-4 --batch_size 128 ...
What Gets Searched:
| Parameter | Default | You Can Override With |
|---|---|---|
| Models | Vector: cnn, resnet18, resnet34; dense: unet_field | --models X Y Z |
| Optimizers | all 6 | --optimizers X Y |
| Schedulers | all 8 | --schedulers X Y |
| Losses | all 6 | --losses X Y |
| Learning rate | 1e-5 → 1e-2 | (always searched) |
| Batch size | Vector: 16, 32, 64, 128; dense: 1, 2, 4, 8 | --batch_sizes N ... |
Search Presets:
| Mode | Vector models | Dense models | Optimizers | Schedulers | Use Case |
|---|---|---|---|---|---|
| Full (default) | cnn, resnet18, resnet34 | unet_field | all 6 | all 8 | Production search |
--medium |
cnn, resnet18 | unet_field | adamw, adam, sgd | plateau, cosine, onecycle | Balanced exploration |
--quick |
cnn | unet_field | adamw | plateau | Fast validation |
Execution Modes:
| Mode | Flag | Pruning | GPU Memory | Best For |
|---|---|---|---|---|
| Subprocess (default) | — | ❌ No | Isolated | Multi-GPU parallel trials |
| In-process | --inprocess |
✅ Yes | Shared | Single-GPU with early stopping |
All Arguments:
| Argument | Default | Description |
|---|---|---|
--data_path |
(required) | Training data file |
--models |
Target-aware | Compatible models to search (specify any number) |
--n_trials |
50 |
Number of trials to run |
--quick |
False |
Quick mode: minimal search space |
--medium |
False |
Medium mode: balanced search space |
--inprocess |
False |
Run trials in-process (enables pruning) |
--optimizers |
all 6 | Optimizers to search |
--schedulers |
all 8 | Schedulers to search |
--losses |
all 6 | Losses to search |
--batch_sizes |
Target-aware | Batch sizes to search |
--n_jobs |
-1 |
Parallel trials (-1 = auto-detect GPUs) |
--max_epochs |
50 |
Max epochs per trial |
--output |
hpo_results.json |
Output file |
See Available Models for all 20+ architectures (70+ variants) you can search.
📈 Data Preparation
WaveDL supports multiple data formats for training and inference:
| Format | Extension | Key Advantages |
|---|---|---|
| NPZ | .npz |
Native NumPy, fast loading, recommended |
| HDF5 | .h5, .hdf5 |
Large datasets, hierarchical, cross-platform |
| MAT | .mat |
MATLAB compatibility (v7.3+ only, saved with -v7.3 flag) |
The framework automatically detects file format and data dimensionality (1D, 2D, or 3D) — you only need to provide the appropriate model architecture.
| Key | Shape | Type | Description |
|---|---|---|---|
input_train / input_test |
(N, L), (N, H, W), or (N, D, H, W) |
float32 |
N samples of 1D/2D/3D representations |
output_train / output_test |
(N,), (N, T), (N, H, W), or (N, C, H, W) |
float32 |
Scalar/vector targets, scalar 2D fields, or channels-first multi-property 2D fields |
Example: Basic Preparation
import numpy as np
X = np.array(images, dtype=np.float32) # (N, H, W)
y = np.array(labels, dtype=np.float32) # (N, T)
np.savez('train_data.npz', input_train=X, output_train=y)
Example: From Image Files + CSV
import numpy as np
from PIL import Image
from pathlib import Path
import pandas as pd
# Load images
images = [np.array(Image.open(f).convert('L'), dtype=np.float32)
for f in sorted(Path("images/").glob("*.png"))]
X = np.stack(images)
# Load labels
y = pd.read_csv("labels.csv").values.astype(np.float32)
np.savez('train_data.npz', input_train=X, output_train=y)
Example: From MATLAB (.mat)
import numpy as np
from scipy.io import loadmat
data = loadmat('simulation_data.mat')
X = data['spectrograms'].astype(np.float32) # Adjust key
y = data['parameters'].astype(np.float32)
# Transpose if needed: (H, W, N) → (N, H, W)
if X.ndim == 3 and X.shape[2] < X.shape[0]:
X = np.transpose(X, (2, 0, 1))
np.savez('train_data.npz', input_train=X, output_train=y)
Example: Synthetic Test Data
import numpy as np
X = np.random.randn(1000, 256, 256).astype(np.float32)
y = np.random.randn(1000, 5).astype(np.float32)
np.savez('test_data.npz', input_test=X, output_test=y)
Validation Script
import numpy as np
data = np.load('train_data.npz')
assert data['input_train'].ndim >= 2, "Input must be at least 2D: (N, ...) "
assert data['output_train'].ndim in (1, 2, 3, 4), \
"Output must be (N,), (N,T), (N,H,W), or (N,C,H,W)"
assert len(data['input_train']) == len(data['output_train']), "Sample mismatch"
print(f"✓ Input: {data['input_train'].shape} {data['input_train'].dtype}")
print(f"✓ Output: {data['output_train'].shape} {data['output_train'].dtype}")
📦 Examples 
The examples/ folder contains a complete, ready-to-run example for material characterization of isotropic plates. The pre-trained MobileNetV3 predicts three physical parameters from Lamb wave dispersion curves:
| Parameter | Unit | Description |
|---|---|---|
| $h$ | mm | Plate thickness |
| $\sqrt{E/\rho}$ | km/s | Square root of Young's modulus over density |
| $\nu$ | — | Poisson's ratio |
Sample Dispersion Data:
Test samples showing the wavenumber-frequency relationship for different plate properties
Try it yourself:
# Run inference on the example data
wavedl-test --checkpoint ./examples/elasticity_prediction/best_checkpoint \
--data_path ./examples/elasticity_prediction/Test_data_100.mat \
--plot --save_predictions --output_dir ./examples/elasticity_prediction/test_results
# Export to ONNX (already included as model.onnx)
wavedl-test --checkpoint ./examples/elasticity_prediction/best_checkpoint \
--data_path ./examples/elasticity_prediction/Test_data_100.mat \
--export onnx --export_path ./examples/elasticity_prediction/model.onnx
What's Included:
| File | Description |
|---|---|
best_checkpoint/ |
Pre-trained MobileNetV3 checkpoint |
Test_data_100.mat |
100 sample test set (500×500 dispersion curves → $h$, $\sqrt{E/\rho}$, $\nu$) |
dispersion_samples.png |
Visualization of sample dispersion curves with material parameters |
model.onnx |
ONNX export with embedded de-normalization |
training_history.csv |
Epoch-by-epoch training metrics (loss, R², LR, etc.) |
training_curves.png |
Training/validation loss and learning rate plot |
test_results/ |
Example predictions and diagnostic plots |
WaveDL_ONNX_Inference.m |
MATLAB script for ONNX inference |
Training Progress:
Training and validation loss with plateau learning rate schedule
Inference Results:
Figure 1: Predictions vs ground truth for all three elastic parameters
Figure 2: Distribution of prediction errors showing near-zero mean bias
Figure 3: Residuals vs predicted values (no heteroscedasticity detected)
Figure 4: Bland-Altman analysis with ±1.96 SD limits of agreement
Figure 5: Q-Q plots confirming normally distributed prediction errors
Figure 6: Error correlation matrix between parameters
Figure 7: Relative error (%) vs true value for each parameter
Figure 8: Cumulative error distribution — 95% of predictions within indicated bounds
Figure 9: True vs predicted values by sample index
Figure 10: Error distribution summary (median, quartiles, outliers)
🔬 Broader Applications
Beyond the material characterization example above, the WaveDL pipeline can be adapted for a wide range of wave-based inverse problems across multiple domains:
🏗️ Non-Destructive Evaluation & Structural Health Monitoring
| Application | Input | Output |
|---|---|---|
| Defect Sizing | A-scans, phased array images, FMC/TFM, ... | Crack length, depth, ... |
| Corrosion Estimation | Thickness maps, resonance spectra, ... | Wall thickness, corrosion rate, ... |
| Weld Quality Assessment | Phased array images, TOFD, ... | Porosity %, penetration depth, ... |
| RUL Prediction | Acoustic emission (AE), vibration spectra, ... | Cycles to failure, ... |
| Damage Localization | Wavefield images, DAS/DVS data, ... | Damage coordinates (x, y, z) |
🌍 Geophysics & Seismology
| Application | Input | Output |
|---|---|---|
| Seismic Inversion | Shot gathers, seismograms, ... | Velocity models, density profiles, ... |
| Subsurface Characterization | Surface wave dispersion, receiver functions, ... | Layer thickness, shear modulus, ... |
| Earthquake Source Parameters | Waveforms, spectrograms, ... | Magnitude, depth, focal mechanism, ... |
| Reservoir Characterization | Reflection seismic, AVO attributes, ... | Porosity, fluid saturation, ... |
🩺 Biomedical Ultrasound & Elastography
| Application | Input | Output |
|---|---|---|
| Tissue Elastography | Shear wave data, strain images, ... | Shear modulus, Young's modulus, ... |
| Liver Fibrosis Staging | Elastography images, US RF data, ... | Stiffness (kPa), fibrosis score, ... |
| Tumor Characterization | B-mode + elastography, ARFI data, ... | Lesion stiffness, size, ... |
| Bone QUS | Axial-transmission signals, ... | Porosity, cortical thickness, elastic modulus ... |
📚 Documentation
| Resource | Description |
|---|---|
| Technical Paper | In-depth framework description (coming soon) |
_template.py |
Template for custom architectures |
📜 Citation
If you use WaveDL in your research, please cite our published paper:
@article{le2026wavedl,
author = {Le, Ductho and Phan, Haidang and Sacchi, Mauricio D. and Le, Lawrence H.},
title = {{WaveDL}: A Scalable Deep Learning Framework for Wave-Based Inverse Problems},
journal = {Computer Physics Communications},
volume = {329},
pages = {110400},
year = {2026},
doi = {10.1016/j.cpc.2026.110400},
url = {https://doi.org/10.1016/j.cpc.2026.110400}
}
Or in APA format:
Le, D., Phan, H., Sacchi, M. D., & Le, L. H. (2026). WaveDL: A scalable deep learning framework for wave-based inverse problems. Computer Physics Communications, 329, 110400. https://doi.org/10.1016/j.cpc.2026.110400
Please also consider to cite other related papers:
@inproceedings{le2026lightweight,
author = {Le, Ductho and Sacchi, Mauricio D. and Zhang, Xu and Ta, Dean and Lou, Edmond and Le, Lawrence H.},
title = {A lightweight deep learning model for ultrasonic assessment of plate thickness and elasticity},
booktitle = {Health Monitoring of Structural and Biological Systems XX},
volume = {13951},
pages = {1395106},
year = {2026},
publisher = {SPIE},
doi = {10.1117/12.3090206},
url = {https://doi.org/10.1117/12.3090206}
}
Or in APA format:
Le, D., Sacchi, M. D., Zhang, X., Ta, D., Lou, E., & Le, L. H. (2026). A lightweight deep learning model for ultrasonic assessment of plate thickness and elasticity. Proc. SPIE 13951, Health Monitoring of Structural and Biological Systems XX, 1395106. https://doi.org/10.1117/12.3090206
🙏 Acknowledgments
Ductho Le would like to acknowledge NSERC and Alberta Innovates for supporting his study and research by means of a research assistantship and a graduate doctoral fellowship.
This research was enabled in part by support provided by Compute Ontario, Calcul Québec, and the Digital Research Alliance of Canada.
Metadata
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For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.
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| File | Size | Uploaded | |
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