Related papers: Discovering Interpretable Physical Models using Sy…

We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or…

TRiSK-type numerical schemes are widely used in both atmospheric and oceanic dynamical cores, due to their discrete analogues of important properties such as energy conservation and steady geostrophic modes. In this work, we show that these…

Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…

Partial Differential Equations (PDEs) have long been recognized as powerful tools for image processing and analysis, providing a framework to model and exploit structural and geometric properties inherent in visual data. Over the years,…

Differential Equation (DE) is a commonly used modeling method in various scientific subjects such as finance and biology. The parameters in DE models often have interesting scientific interpretations, but their values are often unknown and…

Nonlinear dynamics is ubiquitous in nature and commonly seen in various science and engineering disciplines. Distilling analytical expressions that govern nonlinear dynamics from limited data remains vital but challenging. To tackle this…

Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…

Interpretable mathematical expressions defining discrete-time dynamical systems (iterated maps) can model many phenomena of scientific interest, enabling a deeper understanding of system behaviors. Since formulating governing expressions…

Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…

Recently, symbolic regression (SR) has demonstrated its efficiency for discovering basic governing relations in physical systems. A major impact can be potentially achieved by coupling symbolic regression with asymptotic methodology. The…

Modeling the unsaturated behavior of porous materials with multimodal pore size distributions presents significant challenges, as standard hydraulic models often fail to capture their complex, multi-scale characteristics. A common…

Accurate simulations are essential for engineering applications, and intricate continuum mechanical material models are constructed to achieve this goal. However, the increasing complexity of the material models and geometrical properties…

With the advent of modern data collection and storage technologies, data-driven approaches have been developed for discovering the governing partial differential equations (PDE) of physical problems. However, in the extant works the model…

The large time and length scales and, not least, the vast number of particles involved in industrial-scale simulations inflate the computational costs of the Discrete Element Method (DEM) excessively. Coarse grain models can help to lower…

Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…

We introduce a comprehensive data-driven framework aimed at enhancing the modeling of physical systems, employing inference techniques and machine learning enhancements. As a demonstrative application, we pursue the modeling of cathodic…

Data-driven equation discovery aims to reconstruct governing equations directly from empirical observations. A fundamental challenge in this domain is the ill-posed nature of the inverse problem, where multiple distinct mathematical models…

We present Mechanistic PDE Networks -- a model for discovery of governing partial differential equations from data. Mechanistic PDE Networks represent spatiotemporal data as space-time dependent linear partial differential equations in…

We investigate the use of machine learning for solving analytic problems in theoretical physics. In particular, symbolic regression (SR) is making rapid progress in recent years as a tool to fit data using functions whose overall form is…

We present a new method for enhancing symbolic regression for differential equations via dimensional analysis, specifically Ipsen's and Buckingham pi methods. Since symbolic regression often suffers from high computational costs and…