arXiv subjects

Hossein Salahshoor

Publications and source records attributed to Hossein Salahshoor.

7 recordsLinked to original sources

arXiv2026

Multi-field Return Point Memory

Non-equilibrium systems display memory, a dependence not merely on their present environment but on previously applied fields. Multistable systems such as spin glasses, martensites and granular matter have exponentially many microstates consistent with an applied field, making their rich dynamics difficult to control. Control and order can be achieved through the concept of partial ordering, which we here generalize to systems subject to multiple control fields. We demonstrate, within the model system of the zero-temperature Ising model, that this leads to return-point memory, in which an applied sequence of fields restores the hysteretic system not only to a previous magnetization, but to a previous exact microstate. The multiplicity of fields grants more precise and complex control of the system, with different classes of operations displaying commutative and noncommutative behavior. This grants new insight into how physical systems can remember, learn, and be trained.

cond-mat.stat-mech↗

arXiv2026

A Probabilistic Framework for Solving High-Frequency Helmholtz Equations via Diffusion Models

Deterministic neural operators perform well on many PDEs but can struggle with the approximation of high-frequency wave phenomena, where strong input-to-output sensitivity makes operator learning challenging, and spectral bias blurs oscillations. We argue for adopting a probabilistic approach for approximating waves in high-frequency regime, and develop our probabilistic framework using a score-based conditional diffusion operator. After demonstrating a stability analysis of the Helmholtz operator, we present our numerical experiments across a wide range of frequencies, benchmarked against other popular data-driven and machine learning approaches for waves. We show that our probabilistic neural operator consistently produces robust predictions with the lowest errors in $L^2$, $H^1$, and energy norms. Moreover, unlike all the other tested deterministic approaches, our framework remarkably captures uncertainties in the input sound speed map propagated to the solution field. We envision that our results position probabilistic operator learning as a principled and effective approach for solving complex PDEs such as Helmholtz in the challenging high-frequency regime.

cs.LG↗

arXiv2026

Finite Element Eigenfunction Network (FEENet): A Hybrid Framework for Solving PDEs on Complex Geometries

Neural operators aim to learn mappings between infinite-dimensional function spaces, but their performance often degrades on complex or irregular geometries due to the lack of geometry-aware representations. We propose the Finite Element Eigenfunction Network (FEENet), a hybrid spectral learning framework grounded in the eigenfunction theory of differential operators. For a given domain, FEENet leverages the Finite Element Method (FEM)toperformaone-timecomputationofaneigenfunctionbasisintrinsictothegeometry. PDE solutions are subsequently represented in this geometry-adapted basis, and learning is reduced to predicting the corresponding spectral coefficients. Numerical experiments conducted across a range of parameterized PDEs and complex two- and three-dimensional geometries, including benchmarks against the seminal DeepONet framework (1), demonstrate that FEENet consistently achieves superior accuracy and computational efficiency. We further highlight key advantages of the proposed approach, including resolution-independent inference, interpretability, and natural generalization to nonlocal operators defined as functions of differential operators. We envision that hybrid approaches of this form, which combine structure-preserving numerical methods with data-driven learning, offer a promising pathway toward solving real-world PDE problems on complex geometries.

math.NA↗

arXiv2025

Approximating Young Measures With Deep Neural Networks

Parametrized measures (or Young measures) enable to reformulate non-convex variational problems as convex problems at the cost of enlarging the search space from space of functions to space of measures. To benefit from such machinery, we need powerful tools for approximating measures. We develop a deep neural network approximation of Young measures in this paper. The key idea is to write the Young measure as push-forward of Gaussian measures, and reformulate the problem of finding Young measures to finding the corresponding push-forward. We approximate the push-forward map using deep neural networks by encoding the reformulated variational problem in the loss function. After developing the framework, we demonstrate the approach in several numerical examples. We hope this framework and our illustrative computational experiments provide a pathway for approximating Young measures in their wide range of applications from modeling complex microstructure in materials to non-cooperative games.

math.NA↗

arXiv2024

Focal Volume, Acoustic Radiation Force, and Strain in Two-Transducer Regimes

Transcranial focused ultrasound stimulation (TUS) holds promise for non-invasive neural modulation in treating neurological disorders. Most clinically relevant targets are deep within the brain (near or at its geometric center), surrounded by other sensitive regions that need to be spared clinical intervention. However, in TUS, increasing frequency with the goal of improving spatial resolution reduces the effective penetration depth. We show that by using a pair of 1 MHz, orthogonally arranged transducers we improve the spatial resolution afforded by each of the transducers individually, by nearly 40 fold, achieving a sub-cubic millimeter target volume of $0.24\ mm^3$. We show that orthogonally placed transducers generate highly localized standing waves with Acoustic Radiation Force (ARF) arranged into periodic regions of compression and tension near the target. We further present an extended capability of the orthogonal setup, which is to impart selective pressures--either positive or negative, but not both--on the target. Lastly, we share our preliminary findings that strain can arise from both particle motion and ARF with the former reaching its maximum value at the focus, and the latter remaining null at the focus and reaching its maximum around the focus. As the field is investigating the mechanism of interaction in TUS by way of elucidating the mapping between ultrasound parameters and neural response, orthogonal transducers expand our toolbox by making it possible to conduct these investigations at much finer spatial resolutions, with localized and directed (compression vs. tension) ARF and the capability of applying selective pressures at the target.

physics.app-ph↗

arXiv2022

Model-Free Data-Driven Viscoelasticity in the Frequency Domain

We develop a Data-Driven framework for the simulation of wave propagation in viscoelastic solids directly from dynamic testing material data, including data from Dynamic Mechanical Analysis (DMA), nano-indentation, Dynamic Shear Testing (DST) and Magnetic Resonance Elastography (MRE), without the need for regression or material modeling. The problem is formulated in the frequency domain and the method of solution seeks to minimize a distance between physically admissible histories of stress and strain, in the sense of compatibility and equilibrium, and the material data. We metrize the space of histories by means of the flat-norm of their Fourier transform, which allows consideration of infinite wave trains such as harmonic functions. Another significant advantage of the flat norm is that it allows the response of the system at one frequency to be inferred from data at nearby frequencies. We demonstrate and verify the approach by means of two test cases, a polymeric truss structure characterized by DMA data and a 3D soft gel sample characterized by MRE data. The examples demonstrate the ease of implementation of the Data-Driven scheme within conventional commercial codes and its robust convergence properties, both with respect to the solver and the data.

cond-mat.mtrl-sci↗

arXiv2017

Non-Schmid Effects In Perfect Single Crystal Metals At Zero Temperature

A long standing postulate in crystal plasticity of metals is that yielding commences once the resolved shear stress on a slip plane reaches a critical value. This assumption, known as Schmid law, implies that the onset of plasticity is independent of the normal stress acting on the slip plane. We examine the validity of this assumption in single crystal perfect lattices at zero temperature by subjecting them to a wide range of combined normal and shear stresses and identifying the onset of plasticity. We employ phonon stability analysis on four distinct single crystal metals and identify the onset of plasticity with the onset of an instability. Our results show significant dependence of yielding on the normal stress, thereby illustrating the necessity of considering non-Schmid effects in crystal plasticity. Finally, contrary to the common assumption that instabilities in single crystals are of long wavelength type, we show that short wavelength instabilities are abundant in the nucleation of defects for a wide range of loading conditions.

cond-mat.mtrl-sci↗