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The entropy conservative/stable algorithm of Friedrich~\etal (2018) for hyperbolic conservation laws on nonconforming p-refined/coarsened Cartesian grids, is extended to curvilinear grids for the compressible Euler equations. The primary…

In this paper, a backstepping control of the one-phase Stefan Problem, which is a 1-D diffusion Partial Differential Equation (PDE) defined on a time varying spatial domain described by an ordinary differential equation (ODE), is studied. A…

In micro-fluidics not only does capillarity dominate but also thermal fluctuations become important. On the level of the lubrication approximation, this leads to a quasi-linear fourth-order parabolic equation for the film height $h$ driven…

Graph-based surrogate models provide fast alternatives to high-fidelity CFD solvers, but their opaque latent spaces and limited controllability restrict use in safety-critical settings. A key failure mode in oscillatory flows is phase…

We design a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. Although existing nonlinear manifold learning methods seem to be compelling tools to…

While analytical solutions of critical (phase) transitions in physical systems are abundant for simple nonlinear systems, such analysis remains intractable for real-life dynamical systems. A key example of such a physical system is…

Continual Instruction Tuning (CIT) is adopted to continually instruct Large Models to follow human intent data by data. It is observed that existing gradient update would heavily destroy the performance on previous datasets during CIT…

The transport properties at finite temperature of crystalline organic semiconductors are investigated, within the Su-Schrieffer-Heeger model, by combining exact diagonalization technique, Monte Carlo approaches, and maximum entropy method.…

The joint prediction of continuous fields and statistical estimation of the underlying discrete parameters is a common problem for many physical systems, governed by PDEs. Hitherto, it has been separately addressed by employing operator…

The slow iterative sampling nature remains a major bottleneck for the practical deployment of diffusion and flow-based generative models. While consistency models (CMs) represent a state-of-the-art distillation-based approach for efficient…

Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…

Soft robots, distinguished by their inherent compliance and continuum structures, present unique modeling challenges, especially when subjected to significant external loads such as gravity and payloads. In this study, we introduce an…

In this paper, we study the stability of various difference approximations of the Euler-Korteweg equations. This system of evolution PDEs is a classical isentropic Euler system perturbed by a dispersive (third order) term. The Euler…

In this paper, we derive first-order Euler finite element discretization schemes for a time-dependent natural convection model with variable density (NCVD). The model is governed by the variable density Navier-Stokes equations coupled with…

In latent diffusion models, the autoencoder (AE) is typically expected to balance two capabilities: faithful reconstruction and a generation-friendly latent space (e.g., low gFID). In recent ImageNet-scale AE studies, we observe a…

Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…

The understanding of adaptive algorithms for SDEs is an open area where many issues related to both convergence and stability (long time behaviour) of algorithms are unresolved. This paper considers a very simple adaptive algorithm, based…

This paper addresses the local stabilization problem for semilinear single-track vehicle models with distributed tire friction dynamics, represented as interconnections of ordinary differential equations (ODEs) and hyperbolic partial…

In recent years, data-driven deep learning models have gained significant interest in the analysis of turbulent dynamical systems. Within the context of reduced-order models (ROMs), convolutional autoencoders (CAEs) pose a universally…

In collider-based particle and nuclear physics experiments, data are produced at such extreme rates that only a subset can be recorded for later analysis. Typically, algorithms select individual collision events for preservation and store…