scimba 0.5.1

This library implements some common tools for scientific machine learning

ScimBa

This librairies impliment varying SciML methods for varying PDE problem and also tools to build hybrid numerical methods.

Current Content

• Nets: MLP networks, Discontinuous MLP, RBF networks, some activations functions and a basic trainer
• Sampling and domain: general uniform sampling methods for PINNs and Neural Operators. Sampling based on approximated signed distance function for general geometries.
• PDEs: the librairiy implement différent type of model: ODE, spatial pde, times-apce pde, stationary kinetic PDE and kinetic PDE.
• Specific networks for PINNs: For all the equations we implement PINNs networks based on: MLP, Discontinuous MLP and nonlinear radial basis function. We implement also the Fourier network with general features (Fourier but also Gaussian etc)
• Trainer: for each type of PDE we gives a specific trainer.
• Generative Nets: Normalized flows, Gaussian mixture. The classical and conditional approaches are proposed. Trainer based on the maximum likelihood principle.
• Neural Operator: Continuous Auto-encoder based on PointNet encoder and coordinate based decoder. Physic informed DeepOnet for ODE, spatial and time space PDE.
• Neural Galerkin: Method Neural Galerkin for time PDE based on the same network than PINNs.

Ongoing work for 2024

• Nets: New activation function used for implicit representation, Symbolic models, Sindy
• Sampling and domain: learning of signed distance function using PINNs, adaptive sampling
• Specific networks for PINNs: Multiscale architecture, spectral architecture for kinetic, specific architecture.
• Trainer: Trainer with sparsity constraints and globalization method. Loss Balancing
• Generative Nets: Energy models, score matching, more complex normalized flow, Continuous VAE
• Neural Operator: physic informed DeepGreen operator, FNO, GINO based on FNO, NO with neural implicit representation. Kinetic case
• Neural Galerkin: Adaptive sampling, randomization, Least Square solver, implicit scheme. CROM Space time reduced Galerkin model. Greedy basis.

References

PINNs and MLP

• https://www.sciencedirect.com/science/article/abs/pii/S0021999118307125
• https://arxiv.org/abs/2209.03984
• https://arxiv.org/abs/1912.00873
• https://arxiv.org/abs/1912.00873
• https://arxiv.org/abs/2109.01050
• https://arxiv.org/abs/2203.01360
• https://arxiv.org/abs/2103.09959
• https://openreview.net/forum?id=vsMyHUq_C1c

Neural Galerkin

• https://arxiv.org/abs/2306.15630
• https://arxiv.org/abs/2306.03749
• https://arxiv.org/abs/2207.13828
• https://arxiv.org/abs/2201.07953
• https://arxiv.org/abs/2104.13515

DeepOnet

• https://www.nature.com/articles/s42256-021-00302-5
• https://www.science.org/doi/10.1126/sciadv.abi8605
• https://arxiv.org/abs/2205.11404
• https://arxiv.org/abs/2206.03551

FNO and diverse geometry

• https://openreview.net/forum?id=c8P9NQVtmnO
• https://arxiv.org/abs/2207.05209
• https://arxiv.org/abs/2212.04689
• https://arxiv.org/abs/2305.00478
• https://arxiv.org/abs/2306.05697
• https://arxiv.org/abs/2305.19663

Other NO

• https://openreview.net/forum?id=LZDiWaC9CGL
• https://arxiv.org/abs/2205.10573
• https://arxiv.org/abs/2205.02191
• https://openreview.net/forum?id=kIo_C6QmMOM
• https://arxiv.org/abs/2303.10528
• https://arxiv.org/abs/2302.05925

Install the project

git clone https://gitlab.inria.fr/sciml/scimba.git
cd scimba

Install the basic package

pip install -e .

if you want the differential physic aspect we must run:

pip install -e ".[diff_physic]"

Full install

pip install -e ".[all]"

Launch tests

pip install -e ".[test]"
pytest

Generate documentation

pip install -e ".[doc]"
cd docs
env PYTORCH_JIT=0 make html

html docs are generated in _build/html