Learning Dynamics

This repository references papers on learning dynamics from temporal data. We are more precisely concerned with:

• The dynamics: learning $f$ in $\dot{X} = f(X,t)$ from noisy observations $(Y(t_i) = X(t_i) + \varepsilon)_{1\le i \le n}$ and not simply interactions such as $X_1\to X_2$ as in Gene Regulatory Network Inference.
• Mechanistic form: we seek an interpretable form for $f$. Therefore, methods concerned with simply learning $f$ using a neural network or gaussian process are not enough. Typically, one assumes that $f$ takes a parametric form: $f(X,t) \equiv f(X,t,\theta)$, for instance $f_1(X,t,\theta) := \theta_1 X_1 - \theta_2 X_2^2$ would be the parametric vector field of the first variable $X_1$.

We focus mostly on learning ODEs from biological data, but same approaches usually apply to PDEs and other research fields than Biology.

Sparse and SINDy-like methods

• Distilling identifiable and interpretable dynamic models from biological data, 2023
• Automatic differentiation to simultaneously identify nonlinear dynamics and extract noise probability distributions from data, 2022
• Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control, 2022
• Identification of dynamic mass-action biochemical reaction networks using sparse Bayesian methods, 2022
• Gaussian processes meet NeuralODEs: A Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data, 2022
• SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics, 2020
• Reactive SINDy: Discovering governing reactions from concentration data, 2019
• Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics, 2016
• Discovering governing equations from data by sparse identification of nonlinear dynamical systems, 2016

Symbolic regression

• D-CODE: Discovering Closed-form ODEs from Observed Trajectories, 2022
• AI Feynman: A physics-inspired method for symbolic regression, 2020

Others

• Probabilistic grammars for modeling dynamical systems from coarse, noisy, and partial data, 2023
• Differentiable Programming of Chemical Reaction Networks, 2023
• Reactmine: a statistical search algorithm for inferring chemical reactions from time series data, 2022
• On Chemical Reaction Network Design by a Nested Evolution Algorithm, 2019