相关论文: A perturbative solution to metadynamics ordinary d…

We present a data-driven modeling strategy to overcome improperly modeled dynamics for systems exhibiting complex spatio-temporal behaviors. We propose a Deep Learning framework to resolve the differences between the true dynamics of the…

We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…

In this paper, a coherent boundary value problem to model metamaterials' behavior based on the relaxed micromorphic model is established. This boundary value problem includes well-posed boundary conditions, thus disclosing the possibility…

Solving partial differential equations (PDEs) with machine learning typically requires training a new neural network for every new equation. This optimization is slow. We introduce MetaColloc. It is an optimization-free and data-free…

The inverse design of metasurfaces faces inherent challenges due to the nonlinear and highly complex relationship between geometric configurations and their electromagnetic behavior. Traditional optimization approaches often suffer from…

Many problems in physics, material sciences, chemistry and biology can be abstractly formulated as a system that navigates over a complex energy landscape of high or infinite dimensions. Well-known examples include phase transitions of…

In this work we present an adaptive boundary element method for computing the electromagnetic response of wave interactions in hyperbolic metamaterials. One unique feature of hyperbolic metamaterial is the strongly directional wave in its…

Metamaterials are artificial composite structures designed for controlling waves or fields, and exhibit interaction phenomena that are unexpected on the basis of their chemical constituents. These phenomena are encoded in effective material…

This note provides a detailed algorithm to the application of local (perturbation) analysis of differential equations which is normally taught at graduate math courses. Exercise books often present more abstract and simplified versions of…

Glass-forming systems, which are characterized by a highly disordered energy landscape, have been studied in physics by a simulation-based state space aggregation. The purpose of this article is to develop a path-independent approach within…

The now classical replicator equation describes a wide variety of biological phenomena, including those in theoretical genetics, evolutionary game theory, or in the theories of the origin of life. Among other questions, the permanence of…

Dielectric structures composed of many inclusions that manipulate light in ways the bulk materials cannot are commonly seen in the field of metamaterials. In these structures, each inclusion depends on a set of parameters such as location…

This paper is devoted to the study of hyperbolic systems of linear partial differential equations perturbed by a Brownian motion. The existence and uniqueness of solutions are proved by an energy method. The specific features of this class…

In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…

Ultrathin meta-optics offer unmatched, multifunctional control of light. Next-generation optical technologies, however, demand unprecedented performance. This will likely require design algorithms surpassing the capability of human…

Atomistic simulations are widely used to investigate reactive processes but are often limited by the rare event problem due to kinetic bottlenecks. We recently introduced an enhanced sampling approach based on the committor function,…

Approximation techniques have been historically important for solving differential equations, both as initial value problems and boundary value problems. The integration of numerical, analytic and perturbation methods and techniques can…

The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…

Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…

We propose a general variance reduction strategy for diffusion processes. Our approach does not require the knowledge of the measure that is sampled, which may indeed be unknown as for nonequilibrium dynamics in statistical physics. We show…