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This paper presents a neural network--enhanced surrogate modeling approach for diffusion problems with spatially varying random field coefficients. The method builds on numerical homogenization, which compresses fine-scale coefficients into…

Numerical Analysis · Mathematics 2025-09-17 Fabian Kröpfl , Daniel Peterseim , Elisabeth Ullmann

This paper proposes a machine-learning-based solution approach for solving multi-horizon stochastic programs. The approach embeds a deep learning neural network into a multi-horizon stochastic program to approximate the recourse operational…

Optimization and Control · Mathematics 2025-12-03 Hongyu Zhang , Gabriele Sormani , Enza Messina , Alan King , Francesca Maggioni

In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the…

Soft Condensed Matter · Physics 2021-02-11 J. Quetzalcóatl Toledo-Marín , Geoffrey Fox , James P. Sluka , James A. Glazier

We propose a new approach for building recommender systems by adapting surrogate-assisted interactive genetic algorithms. A pool of user-evaluated items is used to construct an approximative model which serves as a surrogate fitness…

Neural and Evolutionary Computing · Computer Science 2019-08-09 Thomas Gabor , Philipp Altmann

The representations of neural networks are often compared to those of biological systems by performing regression between the neural network responses and those measured from biological systems. Many different state-of-the-art deep neural…

Neurons and Cognition · Quantitative Biology 2023-12-13 Abdulkadir Canatar , Jenelle Feather , Albert Wakhloo , SueYeon Chung

Coarse-scale surrogate models in the context of numerical homogenization of linear elliptic problems with arbitrary rough diffusion coefficients rely on the efficient solution of fine-scale sub-problems on local subdomains whose solutions…

Numerical Analysis · Mathematics 2022-09-07 Fabian Kröpfl , Roland Maier , Daniel Peterseim

Network-structured data becomes ubiquitous in daily life and is growing at a rapid pace. It presents great challenges to feature engineering due to the high non-linearity and sparsity of the data. The local and global structure of the…

Machine Learning · Computer Science 2025-01-31 Xin Sun , Zenghui Song , Yongbo Yu , Junyu Dong , Claudia Plant , Christian Boehm

Genotype-to-phenotype mappings translate genotypic variations such as mutations into phenotypic changes. Neutrality is the observation that some mutations do not lead to phenotypic changes. Studying the search trajectories in genotypic and…

Populations and Evolution · Quantitative Biology 2023-06-26 Ting Hu , Gabriela Ochoa , Wolfgang Banzhaf

This work explores hypernetworks: an approach of using a one network, also known as a hypernetwork, to generate the weights for another network. Hypernetworks provide an abstraction that is similar to what is found in nature: the…

Machine Learning · Computer Science 2016-12-02 David Ha , Andrew Dai , Quoc V. Le

Training spiking neural networks to approximate universal functions is essential for studying information processing in the brain and for neuromorphic computing. Yet the binary nature of spikes poses a challenge for direct gradient-based…

Neural and Evolutionary Computing · Computer Science 2024-11-19 Julia Gygax , Friedemann Zenke

Neural generative models can be used to learn complex probability distributions from data, to sample from them, and to produce probability density estimates. We propose a computational framework for developing neural generative models…

Machine Learning · Computer Science 2022-01-06 Alexander Ororbia , Daniel Kifer

Surrogate models driven by sizeable datasets and scientific machine-learning methods have emerged as an attractive microstructure simulation tool with the potential to deliver predictive microstructure evolution dynamics with huge savings…

Materials Science · Physics 2024-01-22 Shaoxun Fan , Andrew L. Hitt , Ming Tang , Babak Sadigh , Fei Zhou

Areas of computational mechanics such as uncertainty quantification and optimization usually involve repeated evaluation of numerical models that represent the behavior of engineering systems. In the case of complex nonlinear systems…

Machine Learning · Computer Science 2024-10-03 A. O. M. Kilicsoy , J. Liedmann , M. A. Valdebenito , F. -J. Barthold , M. G. R. Faes

Simulating the mechanical response of advanced materials can be done more accurately using concurrent multiscale models than with single-scale simulations. However, the computational costs stand in the way of the practical application of…

Machine Learning · Computer Science 2024-02-21 J. Storm , I. B. C. M. Rocha , F. P. van der Meer

Recent work on mode connectivity in the loss landscape of deep neural networks has demonstrated that the locus of (sub-)optimal weight vectors lies on continuous paths. In this work, we train a neural network that serves as a hypernetwork,…

Machine Learning · Statistics 2019-05-09 Lior Deutsch , Erik Nijkamp , Yu Yang

Multitask learning is widely used in practice to train a low-resource target task by augmenting it with multiple related source tasks. Yet, naively combining all the source tasks with a target task does not always improve the prediction…

Machine Learning · Computer Science 2023-12-29 Dongyue Li , Huy L. Nguyen , Hongyang R. Zhang

A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation…

Numerical Analysis · Mathematics 2025-11-04 Matteo Giacomini , Antonio Huerta

Neural networks can be used as surrogates for PDE models. They can be made physics-aware by penalizing underlying equations or the conservation of physical properties in the loss function during training. Current approaches allow to…

Machine Learning · Computer Science 2022-07-01 Raphael Leiteritz , Patrick Buchfink , Bernard Haasdonk , Dirk Pflüger

A significant effort has been made to train neural networks that replicate algorithmic reasoning, but they often fail to learn the abstract concepts underlying these algorithms. This is evidenced by their inability to generalize to data…

Machine Learning · Computer Science 2020-10-26 Yujun Yan , Kevin Swersky , Danai Koutra , Parthasarathy Ranganathan , Milad Hashemi

Evolutionary algorithms are increasingly recognised as a viable computational approach for the automated optimisation of deep neural networks (DNNs) within artificial intelligence. This method extends to the training of DNNs, an approach…

Neural and Evolutionary Computing · Computer Science 2024-03-29 Fergal Stapleton , Brendan Cody-Kenny , Edgar Galván