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We present a contribution to the field of system identification of partial differential equations (PDEs), with emphasis on discerning between competing mathematical models of pattern-forming physics. The motivation comes from developmental…
The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…
Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology, among many others. The physics underlying the patterns is specific to the mechanisms, and is encoded by…
This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable…
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…
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…
We tackle the problem of system identification, where we select inputs, observe the corresponding outputs from the true system, and optimize the parameters of our model to best fit the data. We propose a practical and computationally…
Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…
In this work we present a data-driven method for the discovery of parametric partial differential equations (PDEs), thus allowing one to disambiguate between the underlying evolution equations and their parametric dependencies. Group…
In many problems of data-driven modeling for dynamical systems, the governing equations are not known a priori and must be selected phenomenologically from a large set of candidate interactions and basis functions. In such situations, point…
Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…
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…
This work is concerned with uncertainty quantification in reduced-order dynamical system identification. Reduced-order models for system dynamics are ubiquitous in design and control applications and recent efforts focus on their…
The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…
We propose a two-stage method called \textit{Spline Assisted Partial Differential Equation based Model Identification (SAPDEMI)} to identify partial differential equation (PDE)-based models from noisy data. In the first stage, we employ the…
The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered…
PDE discovery shows promise for uncovering predictive models of complex physical systems but has difficulty when measurements are sparse and noisy. We introduce a new approach for PDE discovery that uses two Rational Neural Networks and a…
We propose a novel method, Phase-IDENT, for identifying partial differential equations (PDEs) from noisy observations of dynamical systems that exhibit phase transitions. Such phenomena are prevalent in fluid dynamics and materials science,…