相关论文: A DeepLagrangian method for learning and generatin…

In this paper we deal with diffusive relaxation limits of nonlinear systems of Euler type modeling chemotactic movement of cells toward Keller--Segel type systems. The approximating systems are either hyperbolic--parabolic or…

Chemotaxis is a fundamental mechanism of cells and organisms, which is responsible for attracting microbes to food, embryonic cells into developing tissues, or immune cells to infection sites. Mathematically chemotaxis is described by the…

The well-suited discretization of the Keller-Segel equations for chemotaxis has become a very challenging problem due to the convective nature inherent to them. This paper aims to introduce a new upwind, mass-conservative, positive and…

The paper that follows describes a numerical algorithm to solve the parabolic-parabolic Keller--Segel system characterized by singular sensitivity and signal absorption in such a manner that the numerical approximations converge towards a…

We derive the divergence-kernel formula for the linear response of random dynamical systems. Specifically, the pathwise expression is for the parameter-derivative of the marginal or stationary density, not an averaged observable. Our…

3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior…

Machine learning (ML) offers considerable promise for the design of new molecules and materials. In real-world applications, the design problem is often domain-specific, and suffers from insufficient data, particularly labeled data, for ML…

Lagrangian algorithms to simulate the evolution of cold dark matter (CDM) are invaluable tools to generate large suites of mock halo catalogues. In this paper, we first show that the main limitation of current semi-analytical schemes to…

The SPARKLING algorithm was originally developed for accelerated 2D magnetic resonance imaging (MRI) in the compressed sensing (CS) context. It yields non-Cartesian sampling trajectories that jointly fulfill a target sampling density while…

The Keller-Segel model is a system of partial differential equations modelling chemotactic aggregation in cellular systems. This model has blowing up solutions for large enough initial conditions in dimensions d >= 2, but all the solutions…

Embedding parameterized optimization problems as layers into machine learning architectures serves as a powerful inductive bias. Training such architectures with stochastic gradient descent requires care, as degenerate derivatives of the…

Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics---particularly for imperfectly-mixed systems. The number of…

We investigate the physics-constrained training of an encoder-decoder neural network for approximating the Fokker-Planck-Landau collision operator in the 5-dimensional kinetic fusion simulation in XGC. To train this network, we propose a…

We rigorously derive a two-dimensional Keller-Segel type system with signal-dependent sensitivity from a stochastic interacting particle model. By employing suitably defined stopping times, we prove that the convergence of the interacting…

We extend the spin-adapted density matrix renormalization group (DMRG) algorithm of McCulloch and Gulacsi [Europhys. Lett.57, 852 (2002)] to quantum chemical Hamiltonians. This involves two key modifications to the non-spin-adapted DMRG…

We propose an input convex neural network (ICNN)-based self-supervised learning framework to solve continuous constrained optimization problems. By integrating the augmented Lagrangian method (ALM) with the constraint correction mechanism,…

Chemotaxis is a fundamental guidance mechanism of cells and organisms, responsible for attracting microbes to food, embryonic cells into developing tissues, immune cells to infection sites, animals towards potential mates, and…

Machine learning has made important headway in helping to improve the treatment of quantum many-body systems. A domain of particular relevance are correlated inhomogeneous systems. What has been missing so far is a general, scalable…

Large pre-trained language models often struggle to incorporate new domain-specific terminology when fine-tuned on small, specialized corpora. In this work, we address the challenge of vocabulary expansion in frozen LLMs by introducing a…

We study a Keller-Segel type chemotaxis model with a modified sensitivity function in a bounded domain $\Omega\subset \mathbb{R}^N$, $N\geq2$. The global existence of classical solutions to the fully parabolic system is established provided…