A package for the sparse identification of nonlinear dynamical systems from data

Pytorch-based framework for solving parametric constrained optimization problems, physics-informed system identification, and parametric model predictive control.

Award winning software library for nonlinear dynamics and nonlinear timeseries analysis

A Python native dynamical system simulation framework in the block diagram paradigm.

pyMOR - Model Order Reduction with Python

Nonlinear Dynamics: A concise introduction interlaced with code

A library for working with Cellular Automata, for Python.

Tools for the exploration of chaos and nonlinear dynamics

A Python module implementing some standard algorithms used in nonlinear time series analysis

Patched Attention for Nonlinear Dynamics [ICLR 2026]

SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics

We discuss nonlinear model predictive control (NMPC) for multi-body dynamics via physics-informed machine learning methods. Physics-informed neural networks (PINNs) are a promising tool to approximate (partial) differential equations. PINNs are not suited for control tasks in their original form since they are not designed to handle variable control actions or variable initial values. We thus present the idea of enhancing PINNs by adding control actions and initial conditions as additional network inputs. The high-dimensional input space is subsequently reduced via a sampling strategy and a zero-hold assumption. This strategy enables the controller design based on a PINN as an approximation of the underlying system dynamics. The additional benefit is that the sensitivities are easily computed via automatic differentiation, thus leading to efficient gradient-based algorithms. Finally, we present our results using our PINN-based MPC to solve a tracking problem for a complex mechanical system, a multi-link manipulator.

nonlinear control optimization tool

An open source model predictive control package for Julia.

Prediction of timeseries using methods of nonlinear dynamics and timeseries analysis

Solve nonlinear heterogeneous agent models

Data-driven reduced order modeling for nonlinear dynamical systems

Python scripts connected to Strogatz's nonlinear dynamics and chaos theory text.

ADRC uses an Extended state observer to linearize the Quadrotor's Nonlinear dynamics (similar to Feedback linearization). This makes it capable of eliminating disturbances (robustness).

A Julia package for solving nonlinear differential equations using the harmonic balance method.

SINDy (Sparse Identification of Nonlinear Dynamics) algorithms

Source code of "Learning nonlinear operators in latent spaces for real-time predictions of complex dynamics in physical systems."

Estimators for probabilities, entropies, and other complexity measures derived from data in the context of nonlinear dynamics and complex systems

An Open Nonlinear Structural Analysis Solver for GNU-Octave or Matlab

A modular and scalable simulation framework for ultra-rapid prototyping of self-adaptive, stochastic and robust Nonlinear Model Predictive Control for Autonomous Vehicle Motion Control

a new observer-based adaptive fuzzy integral sliding mode controller (AFISMC) is proposed based on the Lyapunov stability theorem. The plant under study is subjected to a square-integrable disturbance and is assumed to have mismatch uncertainties both in state- and input-matrices. In addition, a norm-bounded time varying term is introduced to address the possible existence of un-modelled/nonlinear dynamics. Based on the classical sliding mode controller (SMC), the equivalent control effort is obtained to satisfy the sufficient requirement of SMC and then the control law is modified to guarantee the reachability of the system trajectory to the sliding manifold. The sliding surface is compensated based on the observed states in the form of linear matrix inequality (LMI). In order to relax the norm-bounded constrains on the control law and solve the chattering problem of SMC, a fuzzy logic (FL) inference mechanism is combined with the controller. An adaptive law is then introduced to tune the parameters of the fuzzy system on-line. Finally, by aiming at evaluating the validity of the controller and the robust performance of the closed-loop system, the proposed regulator is implemented on a real-time mechanical vibrating system.

Empowering extended Kalman filter (EKF) with Sparse Identification of Nonlinear Dynamics (SINDy)

Fast and simple nonlinear solvers for the SciML common interface. Newton, Broyden, Bisection, Falsi, and more rootfinders on a standard interface.

Material for a full course on applied nonlinear dynamics, nonlinear timeseries analysis, and complex systems, in Julia

Example code for paper: Automatic Differentiation to Simultaneously Identify Nonlinear Dynamics and Extract Noise Probability Distributions from Data