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Neural PDE solvers are increasingly used as learned surrogates for families of partial differential equations, where the key machine learning challenge is not only interpolation on a fixed benchmark distribution but generalization under…
Herein, we present a new data-driven multiscale framework called FE${}^\text{ANN}$ which is based on two main keystones: the usage of physics-constrained artificial neural networks (ANNs) as macroscopic surrogate models and an autonomous…
The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs). It leverages the Fourier Neural Operator to learn solution…
We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…
Composite materials like syntactic foams have complex internal microstructures that manifest high-stress concentrations due to material discontinuities occurring from hollow regions and thin walls of hollow particles or microballoons…
Assumed stress hybrid methods are known to improve the performance of standard displacement-based finite elements and are widely used in computational mechanics. The methods are based on the Hellinger-Reissner variational principle for the…
Flow-field reconstruction from sparse sensor measurements remains a central challenge in modern fluid dynamics, as the need for high-fidelity data often conflicts with practical limits on sensor deployment. Existing deep learning-based…
Accurate real-time prediction of phase-resolved ocean wave fields remains a critical yet largely unsolved problem, primarily due to the absence of practical data assimilation methods for reconstructing initial conditions from sparse or…
Design and analysis of inelastic materials requires prediction of physical responses that evolve under loading. Numerical simulation of such behavior using finite element (FE) approaches can call for significant time and computational…
This study presents the conditional neural fields for reduced-order modeling (CNF-ROM) framework to approximate solutions of parametrized partial differential equations (PDEs). The approach combines a parametric neural ODE (PNODE) for…
Automatic neural architecture design has shown its potential in discovering powerful neural network architectures. Existing methods, no matter based on reinforcement learning or evolutionary algorithms (EA), conduct architecture search in a…
In contrast to the assumptions of most existing Electromigration (EM) analysis tools, the evolution of EM-induced stress is inherently non-deterministic, influenced by factors such as input current fluctuations and manufacturing…
The work is a continuation of a paper by Iskhakov A.S. and Dinh N.T. "Physics-integrated machine learning: embedding a neural network in the Navier-Stokes equations". Part I // arXiv:2008.10509 (2020) [1]. The proposed in [1]…
Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs). However, purely data-driven models often require extensive training data and can generalize poorly, especially in small-data…
Restoring naturalistic finger control in assistive technologies requires the continuous decoding of motor intent with high accuracy, efficiency, and robustness. Here, we present a spike-based decoding framework that integrates spiking…
The aim of this study is to develop a novel WENO scheme that improves the performance of the well-known fifth-order WENO methods. The approximation space consists of exponential polynomials with a tension parameter that may be optimized to…
Physics Informed Machine Learning has emerged as a popular approach for modeling and simulation in digital twins, enabling the generation of accurate models of processes and behaviors in real-world systems. However, existing methods either…
Solving cell problems in homogenization is hard, and available deep-learning frameworks fail to match the speed and generality of traditional computational frameworks. More to the point, it is generally unclear what to expect of…
Accurately simulating systems governed by PDEs, such as voltage fields in cardiac electrophysiology (EP) modelling, remains a significant modelling challenge. Traditional numerical solvers are computationally expensive and sensitive to…
We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…