Solverz 0.11.0

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Solverz is an open-source, general-purpose modeling and simulation toolkit for Python. Define symbolic equations, generate numerical functions or compiled Python modules, and solve your models through a consistent interface.

Installation

Solverz requires Python 3.10 or later.

pip install Solverz

Model types

Solverz supports three equation types.

• Algebraic Equations (AEs) $0=F(y,p)$
• Finite Difference Algebraic Equations (FDAEs) $0=F(y,p,y_0)$
• Differential Algebraic Equations (DAEs) $M\dot{y}=F(t,y,p)$

where $p$ is the parameter set of your models, $y_0$ is the previous time node value of $y$.

A first simulation

The following example models an object launched vertically from the ground. Its velocity and height satisfy

$$ \begin{aligned} &v'=-9.8\ &h'=v \end{aligned} $$

with $v(0)=20$ and $h(0)=0$, we can just type the codes

import matplotlib.pyplot as plt
import numpy as np
from Solverz import Model, Var, Ode, Opt, made_numerical, Rodas

# Declare a simulation model
m = Model()
# Declare variables and equations
m.h = Var('h', 0)
m.v = Var('v', 20)
m.f1 = Ode('f1', f=m.v, diff_var=m.h)
m.f2 = Ode('f2', f=-9.8, diff_var=m.v)
# Create the symbolic equation instance and the variable combination 
bball, y0 = m.create_instance()
# Transform symbolic equations to python numerical functions.
nbball = made_numerical(bball, y0, sparse=True)

# Define events, that is,  if the apple hits the ground then the simulation will cease.
def events(t, y):
    value = np.array([y[0]]) 
    isterminal = np.array([1]) 
    direction = np.array([-1]) 
    return value, isterminal, direction

# Solve the DAE
sol = Rodas(nbball,
            np.linspace(0, 30, 100), 
            y0, 
            Opt(event=events))

# Visualize
plt.plot(sol.T, sol.Y['h'][:, 0])
plt.xlabel('Time/s')
plt.ylabel('h/m')
plt.show()

The result is

Use the numerical interface

The example uses a Rosenbrock method. Solverz also exposes numerical functions for custom solvers. The following Newton–Raphson implementation solves algebraic equations.

@ae_io_parser
def nr_method(eqn: nAE,
              y: np.ndarray,
              opt: Opt = None):
    if opt is None:
        opt = Opt(ite_tol=1e-8)

    tol = opt.ite_tol
    p = eqn.p
    df = eqn.F(y, p)
    ite = 0
    # main loop
    while max(abs(df)) > tol:
        ite = ite + 1
        y = y - solve(eqn.J(y, p), df)
        df = eqn.F(y, p)
        if ite >= 100:
            print(f"Cannot converge within 100 iterations. Deviation: {max(abs(df))}!")
            break

    return aesol(y, ite)

The implementation of the NR solver just resembles the formulae you read in any numerical analysis book. This is because the numerical AE object eqn provides the $F(t,y,p)$ interface and its Jacobian $J(t,y,p)$, which is derived by symbolic differentiation.

Generate a reusable module

Save a model as an independent Python module when you need to reuse it.

from Solverz import module_printer

pyprinter = module_printer(bball,
                           y0,
                           'bounceball',
                           jit=True)
pyprinter.render()

Import the generated model with

from bounceball import mdl as nbball, y as y0

Resources

• Solverz Documentation
• Solverz Cookbook
• Solverz Museum
• Brand assets

Cite Solverz

Chinese

[1] 俞睿智,顾伟,陆帅,张苏涵,徐一骏.面向综合能源系统的开源高性能仿真建模工具开发[J].中国电机工程学报,2026,46(9):3654-3665.DOI:10.13334/j.0258-8013.pcsee.242788.

English

[1] R. Yu, W. Gu, S. Lu, S. Zhang, Y. Xu and R. Wang, "Efficient and Generic Co-simulation Framework for Integrated Energy Systems with Renewable Energy Penetration," 2026 IEEE PES International Meeting (PES IM), Hong Kong, Hong Kong, 2026, pp. 1-5, doi: 10.1109/PESIM67009.2026.11439048.