RNN architectures trained with Backpropagation and Reservoir Computing (RC) methods for forecasting high-dimensional chaotic dynamical systems.

Runge-Kutta adaptive-step solvers for nonlinear PDEs. Solvers include both exponential time differencing and integrating factor methods.

Framework to learn effective dynamics and couple a macro scale simulator with a fast neural network latent propagator.

Numerical Evidence for Sample Efficiency of Model-Based over Model-Free Reinforcement Learning Control of Partial Differential Equations [ECC'24]

pseudospectral (fourier) solutions of a few 1-dimensional PDEs

Spectral Integration and Differentiation Algorithms. Includes FFTs, Chebyshev Transforms, and Hankel transforms. Exponential time differencing and integrating factor Runge-Kutta methods.

An AOT-based algorithm to estimate multiple unknown parameters in the Kuramoto-Saviashinski equation. Source code for the paper "Concurrent Multiparameter Learning Demonstrated on the Kuramoto-Sivashinsky Equation" by Pachev, Whitehead, and McQuarrie.

Julia implementation of cross-scale reservoir computing for high-dimensional spatiotemporal forecasting. Validated on global sea-surface temperature and chaotic dynamics, achieving low error forecasts up to 8 Lyapunov times on Kuramoto-Sivashinsky. Neurocomputing (2026).

Solver for the one dimensional Kuramoto-Sivashinsky using the ETDRK4 method.

Code for the Modeling From Measurements report

A Python package to simulate and measure chaotic dynamical systems.

inZOR-ND: Chaotic systems benchmark — KS_Official structural IID anomaly discovery, +286% improvement (AI-DEEDS 2026)

Este projeto realiza a analise de curvas por meio de elementos finitos das equações de burgers e kuramoto sivashinsky para uma dada condição inicial definida.

ZOR_ESN_Hybrid model for the CTF for Science KS_Official benchmark