Related papers: Learning Stochastic Behaviour from Aggregate Data
The reconstruction and inference of stochastic dynamical systems from data is a fundamental task in inverse problems and statistical learning. While surrogate modeling advances computational methods to approximate these dynamics, standard…
In this work, we study the inverse problem of identifying complex flocking dynamics in a domain cluttered with obstacles. We get inspiration from animal flocks moving in complex ways with capabilities far beyond what current robots can do.…
Training nonlinear parametrizations such as deep neural networks to numerically approximate solutions of partial differential equations is often based on minimizing a loss that includes the residual, which is analytically available in…
An efficient method is presented as a means of an approximate, analytic time-dependent solution of the Fokker-Planck equation (FPE) for the Langevin model subjected to additive and multiplicative noise. We have assumed that the dynamical…
The relaxation to equilibrium in many systems which show strange kinetics is described by fractional Fokker-Planck equations (FFPEs). These can be considered as phenomenological equations of linear nonequilibrium theory. We show that the…
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,…
Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…
Revealing hidden dynamics from the stochastic data is a challenging problem as randomness takes part in the evolution of the data. The problem becomes exceedingly complex when the trajectories of the stochastic data are absent in many…
In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…
Learning physical dynamics from data is a fundamental challenge in machine learning and scientific modeling. Real-world observational data are inherently incomplete and irregularly sampled, posing significant challenges for existing…
In this paper we study the dynamics of a fast-slow Fokker-Planck partial differential equation (PDE) viewed as the evolution equation for the density of a multiscale planar stochastic differential equation (SDE). Our key focus is on the…
The quantitative formulation of evolution equations is the backbone for prediction, control, and understanding of dynamical systems across diverse scientific fields. Besides deriving differential equations for dynamical systems based on…
Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…
Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space…
Many complex phenomena occurring in physics,chemistry, biology, finance, etc. can be reduced, by some projection process, to a 1-d stochastic Differential Equation (SDE) for the variable of interest. Typically, this SDE is both non-linear…
The behavior of many dynamical systems follow complex, yet still unknown partial differential equations (PDEs). While several machine learning methods have been proposed to learn PDEs directly from data, previous methods are limited to…
The Fokker-Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines but it requires specification of the coefficients for each case, which can be functions of space-time and…
The classical Fokker-Planck equation (FPE) is a key tool in physics for describing systems influenced by drag forces and Gaussian noise, with applications spanning multiple fields. We consider the fractional Fokker-Planck equation (FFPE),…
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…
Learning conditional densities and identifying factors that influence the entire distribution are vital tasks in data-driven applications. Conventional approaches work mostly with summary statistics, and are hence inadequate for a…