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Accurate calibration of finite element (FE) models is essential across various biomechanical applications, including human intervertebral discs (IVDs), to ensure their reliability and use in diagnosing and planning treatments. However,…

Neural ordinary differential equations (NODEs) are an effective approach for data-driven modeling of dynamical systems arising from simulations and experiments. One of the major shortcomings of NODEs, especially when coupled with explicit…

Numerical Analysis · Mathematics 2025-12-30 Allen Alvarez Loya , Daniel A. Serino , J. W. Burby , Qi Tang

Solving inverse problems in cardiac electrophysiology consists in the recovery of physiological parameters from surface electrocardiogram (ECG) measurements, a task which is often computationally unfeasible due to the severe ill-posedness…

Numerical Analysis · Mathematics 2026-05-05 Edoardo Centofanti , Giovanni Ziarelli , Simone Scacchi , Luca Franco Pavarino

Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…

Computational Engineering, Finance, and Science · Computer Science 2026-03-30 Timm Gödde , Eisso H. Atzema , Bojana Rosić

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

Numerical Analysis · Mathematics 2020-02-26 Kailai Xu , Eric Darve

This article presents an original methodology for the prediction of steady turbulent aerodynamic fields. Due to the important computational cost of high-fidelity aerodynamic simulations, a surrogate model is employed to cope with the…

Fluid Dynamics · Physics 2019-12-05 Romain Dupuis , Jean-Christophe Jouhaud , Pierre Sagaut

Molecular dynamics simulations are powerful tools to extract the microscopic mechanisms characterizing the properties of soft materials. We recently introduced machine learning surrogates for molecular dynamics simulations of soft materials…

Soft Condensed Matter · Physics 2021-10-29 J. C. S. Kadupitiya , Nasim Anousheh , Vikram Jadhao

In recent years, machine learning approaches to modelling guitar amplifiers and effects pedals have been widely investigated and have become standard practice in some consumer products. In particular, recurrent neural networks (RNNs) are a…

Audio and Speech Processing · Electrical Eng. & Systems 2024-06-11 Alistair Carson , Alec Wright , Jatin Chowdhury , Vesa Välimäki , Stefan Bilbao

There is a high interest in accelerating multiscale models using data-driven surrogate modeling techniques. Creating a large training dataset encompassing all relevant load scenarios is essential for a good surrogate, yet the computational…

Numerical Analysis · Mathematics 2025-04-24 J. Storm , W. Sun , I. B. C. M. Rocha , F. P. van der Meer

Modeling the evolution of physical systems is critical to many applications in science and engineering. As the evolution of these systems is governed by partial differential equations (PDEs), there are a number of computational simulations…

Machine Learning · Computer Science 2025-03-17 Bharat Srikishan , Daniel O'Malley , Mohamed Mehana , Nicholas Lubbers , Nikhil Muralidhar

The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have…

Machine Learning · Computer Science 2025-09-24 Kangzheng Liu , Leixin Ma

Neural controlled differential equations (Neural CDEs) are a continuous-time extension of recurrent neural networks (RNNs), achieving state-of-the-art (SOTA) performance at modelling functions of irregular time series. In order to interpret…

Machine Learning · Computer Science 2021-06-22 James Morrill , Patrick Kidger , Lingyi Yang , Terry Lyons

We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…

Numerical Analysis · Mathematics 2022-02-28 Elizabeth Qian , Ionut-Gabriel Farcas , Karen Willcox

Surrogate models provide compact relations between user-defined input parameters and output quantities of interest, enabling the efficient evaluation of complex parametric systems in many-query settings. Such capabilities are essential in a…

Numerical Analysis · Mathematics 2026-03-16 Matteo Giacomini , Pedro Díez

By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…

Machine Learning · Computer Science 2020-10-19 Daehoon Gwak , Gyuhyeon Sim , Michael Poli , Stefano Massaroli , Jaegul Choo , Edward Choi

The problem of varying dynamics of tracked objects, such as pedestrians, is traditionally tackled with approaches like the Interacting Multiple Model (IMM) filter using a Bayesian formulation. By following the current trend towards using…

Computer Vision and Pattern Recognition · Computer Science 2019-04-29 Stefan Becker , Ronny Hug , Wolfgang Hübner , Michael Arens

Multi-agent trajectory prediction is crucial for various practical applications, spurring the construction of many large-scale trajectory datasets, including vehicles and pedestrians. However, discrepancies exist among datasets due to…

Computer Vision and Pattern Recognition · Computer Science 2023-12-27 Daehee Park , Jaewoo Jeong , Kuk-Jin Yoon

Developing surrogates for computer models has become increasingly important for addressing complex problems in science and engineering. This article introduces an artificial intelligent (AI) surrogate, referred to as the DeepSurrogate, for…

To preserve strictly conservative behavior as well as model the variety of dissipative behavior displayed by solid materials, we propose a significant enhancement to the internal state variable-neural ordinary differential equation…

Materials Science · Physics 2025-02-21 Reese E. Jones , Jan N. Fuhg

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,…

Fluid Dynamics · Physics 2024-11-20 Dashan Zhang , Yuntian Chen , Shiyi Chen