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POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality…

Numerical Analysis · Mathematics 2023-05-09 Simone Brivio , Stefania Fresca , Nicola Rares Franco , Andrea Manzoni

I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…

Machine Learning · Statistics 2026-01-09 James Rice

We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…

Computational Physics · Physics 2020-05-20 Ariana Mendible , Steven L. Brunton , Aleksandr Y. Aravkin , Wes Lowrie , J. Nathan Kutz

As power systems transition toward renewable-rich and inverter-dominated operations, accurate time-domain dynamic analysis becomes increasingly critical. Such analysis supports key operational tasks, including transient stability…

Artificial Intelligence · Computer Science 2026-04-17 Haoran Li , Lihao Mai , Chenhan Xiao , Erik Blasch , Yang Weng

Reduced-order modeling (ROM) of time-dependent and parameterized differential equations aims to accelerate the simulation of complex high-dimensional systems by learning a compact latent manifold representation that captures the…

Machine Learning · Computer Science 2025-10-28 Nima Hosseini Dashtbayaz , Hesam Salehipour , Adrian Butscher , Nigel Morris

Generative models are spearheading recent progress in deep learning, showcasing strong promise for trajectory sampling in dynamical systems as well. However, whereas latent space modeling paradigms have transformed image and video…

Machine Learning · Computer Science 2026-01-16 Florian Sestak , Artur Toshev , Andreas Fürst , Günter Klambauer , Andreas Mayr , Johannes Brandstetter

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc.…

Numerical Analysis · Mathematics 2024-02-06 Zhanhong Ye , Xiang Huang , Hongsheng Liu , Bin Dong

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…

Fluid Dynamics · Physics 2025-03-26 Ashish S. Nair , Shivam Barwey , Pinaki Pal , Jonathan F. MacArt , Troy Arcomano , Romit Maulik

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

Computational Engineering, Finance, and Science · Computer Science 2021-09-24 Thomas Simpson , Nikolaos Dervilis , Eleni Chatzi

The simulation of many complex phenomena in engineering and science requires solving expensive, high-dimensional systems of partial differential equations (PDEs). To circumvent this, reduced-order models (ROMs) have been developed to speed…

Machine Learning · Computer Science 2025-10-27 Paolo Conti , Jonas Kneifl , Andrea Manzoni , Attilio Frangi , Jörg Fehr , Steven L. Brunton , J. Nathan Kutz

Learning or identifying dynamics from a sequence of high-dimensional observations is a difficult challenge in many domains, including reinforcement learning and control. The problem has recently been studied from a generative perspective…

Robotics · Computer Science 2022-07-12 Oliver Limoyo , Bryan Chan , Filip Marić , Brandon Wagstaff , Rupam Mahmood , Jonathan Kelly

A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…

Machine Learning · Computer Science 2024-12-02 Zan Ahmad , Shiyi Chen , Minglang Yin , Avisha Kumar , Nicolas Charon , Natalia Trayanova , Mauro Maggioni

Learning from Demonstration (LfD) techniques enable robots to learn and generalize tasks from user demonstrations, eliminating the need for coding expertise among end-users. One established technique to implement LfD in robots is to encode…

Latent ODE models provide flexible descriptions of dynamic systems, but they can struggle with extrapolation and predicting complicated non-linear dynamics. The latent ODE approach implicitly relies on encoders to identify unknown system…

Machine Learning · Computer Science 2024-10-14 Matt L. Sampson , Peter Melchior

We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an…

Machine Learning · Computer Science 2023-10-27 Valerii Iakovlev , Markus Heinonen , Harri Lähdesmäki

High-dimensional observations and unknown dynamics are major challenges when applying optimal control to many real-world decision making tasks. The Learning Controllable Embedding (LCE) framework addresses these challenges by embedding the…

Machine Learning · Computer Science 2020-03-03 Rui Shu , Tung Nguyen , Yinlam Chow , Tuan Pham , Khoat Than , Mohammad Ghavamzadeh , Stefano Ermon , Hung H. Bui

With the rapid proliferation of autonomous driving, there has been a heightened focus on the research of lidar-based 3D semantic segmentation and object detection methodologies, aiming to ensure the safety of traffic participants. In recent…

Computer Vision and Pattern Recognition · Computer Science 2024-06-13 Jiahua Xu , Si Zuo , Chenfeng Wei , Wei Zhou

How can we build surrogate solvers that train on small domains but scale to larger ones without intrusive access to PDE operators? Inspired by the Data-Driven Finite Element Method (DD-FEM) framework for modular data-driven solvers, we…

Dynamical Systems · Mathematics 2026-01-06 Seung Whan Chung , Youngsoo Choi , Christopher Miller , H. Keo Springer , Kyle T. Sullivan

Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper…

Systems and Control · Electrical Eng. & Systems 2024-09-12 Priyabrata Saha , Saibal Mukhopadhyay

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…

Machine Learning · Computer Science 2025-10-29 Sharmila Karumuri , Lori Graham-Brady , Somdatta Goswami