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One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs). We address this problem by taking advantage of recent advances in scientific machine learning and…
Numerical simulation of viscoelastic flows is challenging because of the hyperbolic nature of viscoelastic constitutive equations. Despite their superior accuracy and efficiency, pseudo-spectral methods require the introduction of…
Ensuring the safe and reliable operation of integrated electricity and gas systems (IEGS) requires dynamic energy flow (DEF) simulation tools that achieve high accuracy and computational efficiency. However, the inherent strong nonlinearity…
Following an original idea of F. Guerra, in this notes we analyze the Sherrington-Kirkpatrick model from different perspectives, all sharing the underlying approach which consists in linking the resolution of the statistical mechanics of…
Spiking Neural Networks (SNNs), with their brain-inspired spatiotemporal dynamics and spike-driven computation, have emerged as promising energy-efficient alternatives to Artificial Neural Networks (ANNs). However, existing SNNs typically…
A time-dependent formulation for electron-hole excitations in extended finite systems, based on the Bethe-Salpeter equation (BSE), is developed using a stochastic wave function approach. The time-dependent formulation builds on the…
The neural dynamics underlying brain activity are critical to understanding cognitive processes and mental disorders. However, current voxel-based whole-brain dimensionality reduction techniques fall short of capturing these dynamics,…
Neuromorphic hardware as a non-Von Neumann architecture has better energy efficiency and parallelism than the conventional computer. Here, with numerical modeling spin-orbit torque (SOT) device using current-induced SOT and Joule heating…
This study proposes a novel deep-learning-based method for generating reduced representations of turbulent flows that ensures efficient storage and transfer while maintaining high accuracy during decompression. A Swin-Transformer network…
We propose an analytical thermodynamic model for describing defect phase transformations, which we term the statistical phase evaluation approach (SPEA). The SPEA model assumes a Boltzmann distribution of finite size phase fractions and…
In this paper we discuss the potential of emerging spintorque devices for computing applications. Recent proposals for spinbased computing schemes may be differentiated as all-spin vs. hybrid, programmable vs. fixed, and, Boolean vs.…
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…
The applicability of the highly idealized secondary infall model to `realistic' initial conditions is investigated. The collapse of proto-halos seeded by $3\sigma$ density perturbations to an Einstein--de Sitter universe is studied here for…
Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…
Partial Differential Equations (PDEs) are the bedrock for modern computational sciences and engineering, and inherently computationally expensive. While PDE foundation models have shown much promise for simulating such complex…
Dynamic impact analysis is a fundamental technique for understanding the impact of specific program entities, or changes to them, on the rest of the program for concrete executions. However, existing techniques are either inapplicable or of…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…
We present a new formulation of the correlated electron-ion dynamics (CEID) scheme, which systematically improves Ehrenfest dynamics by including quantum fluctuations around the mean-field atomic trajectories. We show that the method can…
This work aims to estimate the drift and diffusion functions in stochastic differential equations (SDEs) driven by a particular class of L\'evy processes with finite jump intensity, using neural networks. We propose a framework that…