Related papers: PriorIDENT: Prior-Informed PDE Identification from…

This work presents a data-driven approach to the identification of spatial and temporal truncation errors for linear and nonlinear discretization schemes of Partial Differential Equations (PDEs). Motivated by the central role of truncation…

Control in fluid environments is an important research area with numerous applications across various domains, including underwater robotics, aerospace engineering, and biomedical systems. However, in practice, control methods often face…

Denoising diffusion probabilistic models have been recently proposed to generate high-quality samples by estimating the gradient of the data density. The framework defines the prior noise as a standard Gaussian distribution, whereas the…

Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…

In scientific machine learning, the task of identifying partial differential equations accurately from sparse and noisy data poses a significant challenge. Current sparse regression methods may identify inaccurate equations on sparse and…

Diffusion-based solvers for partial differential equations (PDEs) are often bottle-necked by slow gradient-based test-time optimization routines that use PDE residuals for loss guidance. They additionally suffer from optimization…

Robust physics discovery is of great interest for many scientific and engineering fields. Inspired by the principle that a representative model is the one simplest possible, a new model selection criteria considering both model's Parsimony…

Data-driven discovery of governing equations from time-series data provides a powerful framework for understanding complex biological systems. Library-based approaches that use sparse regression over candidate functions have shown…

Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real-world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore,…

Delay Differential Equations (DDEs) are a class of differential equations that can model diverse scientific phenomena. However, identifying the parameters, especially the time delay, that make a DDE's predictions match experimental results…

This paper presents a machine learning framework (GP-NODE) for Bayesian systems identification from partial, noisy and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in…

Learned image compression (LIC) has achieved remarkable coding efficiency, where entropy modeling plays a pivotal role in minimizing bitrate through informative priors. Existing methods predominantly exploit internal contexts within the…

This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…

Data assimilation (DA) for systems governed by partial differential equations (PDE) aims to reconstruct full spatiotemporal fields from sparse high-fidelity (HF) observations while respecting physical constraints. While full-grid…

The core challenge of hyperspectral image denoising is striking the right balance between data fidelity and noise prior modeling. Most existing methods place too much emphasis on the intrinsic priors of the image while overlooking diverse…

Data-driven discovery of partial differential equations (PDEs) from observed data in machine learning has been developed by embedding the discovery problem. Recently, the discovery of traditional ODEs dynamics using linear multistep methods…

Recent work in data-driven modeling has demonstrated that a weak formulation of model equations enhances the noise robustness of a wide range of computational methods. In this paper, we demonstrate the power of the weak form to enhance the…

Data-driven identification of partial differential equations (PDEs) relies on sparse regression over a candidate library of differential operators, where larger libraries inflate false positives under observation noise and smaller libraries…

Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…