Related papers: Learning Differential Operators for Interpretable …

This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning…

Time series forecasting in real-world applications requires both high predictive accuracy and interpretable uncertainty quantification. Traditional point prediction methods often fail to capture the inherent uncertainty in time series data,…

This paper explores the efficacy of diffusion-based generative models as neural operators for partial differential equations (PDEs). Neural operators are neural networks that learn a mapping from the parameter space to the solution space of…

Modeling dynamical systems is crucial across the science and engineering fields for accurate prediction, control, and decision-making. Recently, machine learning (ML) approaches, particularly neural ordinary differential equations (NODEs),…

By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been…

Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…

Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We…

Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…

In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for learning Hamiltonian mechanics, methods based on deep…

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…

Neural differential equation models have garnered significant attention in recent years for their effectiveness in machine learning applications.Among these, fractional differential equations (FDEs) have emerged as a promising tool due to…

Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…

A core problem in machine learning is to learn expressive latent variables for model prediction on complex data that involves multiple sub-components in a flexible and interpretable fashion. Here, we develop an approach that improves…

This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…

Artificial neural networks, widely recognised for their role in machine learning, are now transforming the study of ordinary differential equations (ODEs), bridging data-driven modelling with classical dynamical systems and enabling the…

The objective of this proposal is to bridge the gap between Deep Learning (DL) and System Dynamics (SD) by developing an interpretable neural system dynamics framework. While DL excels at learning complex models and making accurate…

Inverse problems involving partial differential equations (PDEs) can be seen as discovering a mapping from measurement data to unknown quantities, often framed within an operator learning approach. However, existing methods typically rely…

Physical dynamical systems can be viewed as natural information processors: their systems preserve, transform, and disperse input information. This perspective motivates learning not only from data generated by such systems, but also how to…

Modeling nonlinear spatiotemporal dynamical systems has primarily relied on partial differential equations (PDEs). However, the explicit formulation of PDEs for many underexplored processes, such as climate systems, biochemical reaction and…

Time series data is prevalent in a wide variety of real-world applications and it calls for trustworthy and explainable models for people to understand and fully trust decisions made by AI solutions. We consider the problem of building…