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The constitutive behavior of polymeric materials is often modeled by finite linear viscoelastic (FLV) or quasi-linear viscoelastic (QLV) models. These popular models are simplifications that typically cannot accurately capture the nonlinear…
One of the ultimate goals of computational modeling in condensed matter is to be able to accurately compute materials properties with minimal empirical information. First-principles approaches such as the density functional theory (DFT)…
Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…
We consider collections of $N$ chordal random curves obtained from a critical lattice model on a planar graph, in the limit when a fine-mesh graph approximates a simply-connected domain. We define and study candidates for such limits in…
This paper introduces new parameterizations of equilibrium neural networks, i.e. networks defined by implicit equations. This model class includes standard multilayer and residual networks as special cases. The new parameterization admits a…
Interpretability is crucial for ensuring RL systems align with human values. However, it remains challenging to achieve in complex decision making domains. Existing methods frequently attempt interpretability at the level of fundamental…
We consider the plasma confined in a general axisymmetric spatial domain with perfect conducting boundary which reflects particles specularly, and look at a certain class of equilibria, assuming axisymmetry in the problem. We prove a sharp…
Recent experiments on temporal reflection in transmission line metamaterials and theoretical treatments of dispersive time-varying media have unearthed the fundamental role of modulation mechanisms on the interface conditions, underpinning…
We introduce a general model which augments the one-dimensional nonlinear Schr\"{o}dinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a…
To derive bounds on the strain and stress response of a two-component composite material with viscoelastic phases, we revisit the so-called analytic method (Bergman 1978), which allows one to approximate the complex effective tensor,…
Diffusion models have demonstrated remarkable capabilities in synthesizing realistic images, spurring interest in using their representations for various downstream tasks. To better understand the robustness of these representations, we…
Expanding the use of physical degrees of freedom to employ spatial multiplexing of data in optical communication is considered the most disruptive and effective solution to meet the capacity demand of the growing information traffic.…
The linear (Winkler) foundation is a simple model widely used for decades to account for the surface response of elastic bodies. It models the response as purely local, linear, and perpendicular to the surface. We extend this model to the…
While there has been increasing interest in using neural networks to compute Lyapunov functions, verifying that these functions satisfy the Lyapunov conditions and certifying stability regions remain challenging due to the curse of…
We establish the convergence of physics-informed neural networks (PINNs) for time-dependent fractional diffusion equations posed on bounded domains. The presence of fractional Laplacian operators introduces nonlocal behavior and regularity…
We study the quantum affine superalgebra $U_q(Lsl(M,N))$ and its finite-dimensional representations. We prove a triangular decomposition and establish a system of Poincar\'{e}-Birkhoff-Witt generators for this superalgebra, both in terms of…
Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…
Identification and parameterisation of constitutive models can be a challenging task in rheology. We investigate the use of Random Forest (RF) regression to estimate viscoelastic constitutive model parameters using Large Amplitude…
A lattice model of critical dense polymers is solved exactly for finite strips. The model is the first member of the principal series of the recently introduced logarithmic minimal models. The key to the solution is a functional equation in…
The usual approach to model reduction for parametric partial differential equations (PDEs) is to construct a linear space $V_n$ which approximates well the solution manifold $\mathcal{M}$ consisting of all solutions $u(y)$ with $y$ the…