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This paper addresses some fundamental issues in nonconvex analysis. By using pure complementary energy principle proposed by the author, a class of fully nonlinear partial diforerential equations in nonlinear elasticity is able to converted…
The variational approach to fracture is effective for simulating the nucleation and propagation of complex crack patterns, but is computationally demanding. The model is a strongly nonlinear non-convex variational inequality that demands…
Low-precision quantization is recognized for its efficacy in neural network optimization. Our analysis reveals that non-quantized elementwise operations which are prevalent in layers such as parameterized activation functions, batch…
In recent years, there has been a growing interest in leveraging deep learning and neural networks to address scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods…
Non-commutative polynomial optimization is a powerful technique with numerous applications in quantum nonlocality, quantum key distribution, causal inference, many-body physics, amongst others. The standard approach is to reduce such…
We present MADLens a python package for producing non-Gaussian lensing convergence maps at arbitrary source redshifts with unprecedented precision. MADLens is designed to achieve high accuracy while keeping computational costs as low as…
We present a novel physics-informed system identification method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the input, state, and output of a system in the…
High-dimensional recordings of dynamical processes are often characterized by a much smaller set of effective variables, evolving on low-dimensional manifolds. Identifying these latent dynamics requires solving two intertwined problems:…
Comparing with the classical local gradient flow and phase field models, the nonlocal models such as nonlocal Cahn-Hilliard equations equipped with nonlocal diffusion operator can describe more practical phenomena for modeling phase…
Non-linear differential equations are a fundamental tool to describe different phenomena in nature. However, we still lack a well-established method to tackle stiff differential equations. Here we present a machine learning framework to…
We explore an application of the Physics Informed Neural Networks (PINNs) in conjunction with Airy stress functions and Fourier series to find optimal solutions to a few reference biharmonic problems of elasticity and elastic plate theory.…
Large language models (LLMs) excel in many natural language tasks, yet they struggle with complex mathemat-ical problem-solving, particularly in symbolic reasoning and maintaining consistent output. This study evalu-ates 10 LLMs with 7 to 8…
Nonlinear models are known to provide excellent performance in real-world applications that often operate in non-ideal conditions. However, such applications often require online processing to be performed with limited computational…
Photonic neural networks offer a promising alternative to traditional electronic systems for machine learning accelerators due to their low latency and energy efficiency. However, the challenge of implementing the backpropagation algorithm…
We consider a system of nonlinear ordinary differential equations for the solution of linear programming (LP) problems that was first proposed in the mathematical biology literature as a model for the foraging behavior of acellular slime…
Quantum Monte Carlo methods are powerful tools for studying quantum many-body systems but face difficulties in accessing excited states and in treating sign problems. We present a continuous-time path-integral Monte Carlo method for…
As renewable energy integration, sector coupling, and spatiotemporal detail increase, energy system optimization models grow in size and complexity, often pushing solvers to their performance limits. This systematic review explores…
This article is devoted to the study of certain models for phase transitions involving nonlocal energies. A first part is concerned with to the asymptotic analysis of a system of fractional elliptic equations of Allen-Cahn type as a…
We propose an effective and flexible way to implement 2D and 3D elastoplastic problems in MATLAB using fully vectorized codes. Our technique is applied to a broad class of the problems including perfect plasticity or plasticity with…
Patriksson (2008) provided a then up-to-date survey on the continuous,separable, differentiable and convex resource allocation problem with a single resource constraint. Since the publication of that paper the interest in the problem has…