Related papers: Governing equation discovery of a complex system f…

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…

The measured spatiotemporal response of various physical processes is utilized to infer the governing partial differential equations (PDEs). We propose SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE), a technique…

We show how a complete mathematical description of a complicated physical phenomenon can be learned from observational data via a hybrid approach combining three simple and general ingredients: physical assumptions of smoothness, locality,…

Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…

We propose a novel Skew Gradient Embedding (SGE) framework for systematically reformulating thermodynamically consistent partial differential equation (PDE) models-capturing both reversible and irreversible processes-as generalized gradient…

Many chemical engineering systems are governed by mechanisms that switch across operating regimes, making the data-driven discovery of regime-dependent governing equations essential for predictive modeling, optimization, and control. We…

Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations…

We introduce a lattice random walk discretisation scheme for stochastic differential equations (SDEs) that samples binary or ternary increments at each step, suppressing complex drift and diffusion computations to simple 1 or 2 bit random…

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions,…

Score-based generative models based on stochastic differential equations (SDEs) achieve impressive performance in sampling from unknown distributions, but often fail to satisfy underlying constraints. We propose a constrained generative…

The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…

This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…

Ordinary differential equations (ODE) have been widely used for modeling dynamical complex systems. For high-dimensional ODE models where the number of differential equations is large, it remains challenging to estimate the ODE parameters…

The data-driven models allow one to define the model structure in cases when a priori information is not sufficient to build other types of models. The possible way to obtain physical interpretation is the data-driven differential equation…

Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating…

We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linear combination of a few linear and nonlinear differential…

The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift,…

The combination of machine learning (ML) and sparsity-promoting techniques is enabling direct extraction of governing equations from data, revolutionizing computational modeling in diverse fields of science and engineering. The discovered…

System identification plays a crucial role in physics and machine learning for discovering governing equations directly from data. A powerful approach is the Sparse Identification of Nonlinear Dynamics (SINDy) method, which assumes that…