Related papers: Identification of Partial-Differential-Equations-B…
We introduce a Monte Carlo method for computing derivatives of the solution to a partial differential equation (PDE) with respect to problem parameters (such as domain geometry or boundary conditions). Derivatives can be evaluated at…
This paper proposes a novel fault detection and isolation (FDI) scheme for distributed parameter systems modeled by a class of parabolic partial differential equations (PDEs) with nonlinear uncertain dynamics. A key feature of the proposed…
This work leverages laser vibrometry and the weak form of the sparse identification of nonlinear dynamics (WSINDy) for partial differential equations to learn macroscale governing equations from full-field experimental data. In the…
Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters,…
PySINDy is a Python package for the discovery of governing dynamical systems models from data. In particular, PySINDy provides tools for applying the sparse identification of nonlinear dynamics (SINDy) (Brunton et al. 2016) approach to…
This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…
We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surrogate models of the fine scale dynamics. We approximate the…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
This paper presents a novel approach for numerical solution of a class of fourth order time fractional partial differential equations (PDE's). The finite difference formulation has been used for temporal discretization, whereas, the space…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for the numerical solution of partial differential equations. We start with a detailed explanation of the method for the…
Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…
Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…
In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…
Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…
In this work we study the problem about learning a partial differential equation (PDE) from its solution data. PDEs of various types are used as examples to illustrate how much the solution data can reveal the PDE operator depending on the…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…
In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…