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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…

In this paper we introduce a novel way of estimating prediction uncertainty in deep networks through the use of uncertainty surrogates. These surrogates are features of the penultimate layer of a deep network that are forced to match…

Machine Learning · Computer Science 2021-04-19 Radhakrishna Achanta , Natasa Tagasovska

Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…

Numerical Analysis · Mathematics 2025-01-28 Qi Wang , Yuan Mi , Haoyun Wang , Yi Zhang , Ruizhi Chengze , Hongsheng Liu , Ji-Rong Wen , Hao Sun

Neural networks have promise as surrogate partial differential equation (PDE) solvers, but it remains a challenge to use these concepts to solve problems with high accuracy and scalability. In this work, we show that neural network…

Computational Physics · Physics 2025-09-05 Chenkai Mao , Jonathan A. Fan

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

Numerical Analysis · Mathematics 2025-03-10 Mingxing Weng , Zhiping Mao , Jie Shen

Recent years have seen a surge in deep learning approaches to accelerate numerical solvers, which provide faithful but computationally intensive simulations of the physical world. These deep surrogates are generally trained in a supervised…

Machine Learning · Computer Science 2023-10-02 Lucas Meyer , Marc Schouler , Robert Alexander Caulk , Alejandro Ribés , Bruno Raffin

Multiscale problems are widely observed across diverse domains in physics and engineering. Translating these problems into numerical simulations and solving them using numerical schemes, e.g. the finite element method, is costly due to the…

Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…

Machine Learning · Computer Science 2025-03-31 Zijie Li , Anthony Zhou , Amir Barati Farimani

The computational resources required to solve the full 3D inversion of time-domain electromagnetic data are immense. To overcome the time-consuming 3D simulations, we construct a surrogate model, more precisely, a data-driven statistical…

Geophysics · Physics 2024-07-10 Wouter Deleersnyder , David Dudal , Thomas Hermans

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

Accurate modeling of physical systems governed by partial differential equations is a central challenge in scientific computing. In oceanography, high-resolution current data are critical for coastal management, environmental monitoring,…

Machine Learning · Computer Science 2025-10-21 Abdessamad El-Kabid , Loubna Benabbou , Redouane Lguensat , Alex Hernández-García

Large-scale numerical simulations are used across many scientific disciplines to facilitate experimental development and provide insights into underlying physical processes, but they come with a significant computational cost. Deep neural…

Scientific computing for large deformation of elastic-plastic solids is critical for numerous real-world applications. Classical numerical solvers rely primarily on local discrete linear approximation and are constrained by an inherent…

Machine Learning · Computer Science 2025-06-09 Shilong Tao , Zhe Feng , Haonan Sun , Zhanxing Zhu , Yunhuai Liu

Neural networks have emerged as powerful surrogates for solving partial differential equations (PDEs), offering significant computational speedups over traditional methods. However, these models suffer from a critical limitation: error…

Machine Learning · Computer Science 2025-12-29 Xinquan Huang , Paris Perdikaris

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

Machine Learning · Computer Science 2019-11-22 Jonathan B. Freund , Jonathan F. MacArt , Justin Sirignano

We present a scalable framework for learning deterministic and probabilistic neural surrogates for high-resolution 3D physics simulations. We introduce a hybrid CNN-Transformer backbone architecture targeted for 3D physics simulations,…

Machine Learning · Computer Science 2025-10-09 Benjamin Holzschuh , Georg Kohl , Florian Redinger , Nils Thuerey

The dominant paradigm for power system dynamic simulation is to build system-level simulations by combining physics-based models of individual components. The sheer size of the system along with the rapid integration of inverter-based…

Systems and Control · Electrical Eng. & Systems 2024-10-24 Matthew Bossart , Jose Daniel Lara , Ciaran Roberts , Rodrigo Henriquez-Auba , Duncan Callaway , Bri-Mathias Hodge

Surrogate neural network-based partial differential equation (PDE) solvers have the potential to solve PDEs in an accelerated manner, but they are largely limited to systems featuring fixed domain sizes, geometric layouts, and boundary…

Machine Learning · Computer Science 2025-01-10 Chenkai Mao , Robert Lupoiu , Tianxiang Dai , Mingkun Chen , Jonathan A. Fan

Numerically solving a large parametric nonlinear dynamical system is challenging due to its high complexity and the high computational costs. In recent years, machine-learning-aided surrogates are being actively researched. However, many…

Machine Learning · Computer Science 2024-10-18 Shuwen Sun , Lihong Feng , Peter Benner

Poroelasticity -- coupled fluid flow and elastic deformation in porous media -- often involves spatially variable permeability, especially in subsurface systems. In such cases, simulations with random permeability fields are widely used for…

Machine Learning · Computer Science 2025-09-16 Sangjoon Park , Yeonjong Shin , Jinhyun Choo