A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Proposes a new model for traffic flow on directed graphs.
Modeling bone microarchitecture adaptation using geometric flows.
In this work, we extend existing well-posedness by noise results for the stochastic transport and continuity equations by treating them as special cases of the linear advection equation of -forms, which arises naturally in geometric fluid dynamics. In particular, we prove the existence and uniqueness of weak -s…
This work analyzes PINNs for advection-diffusion equations using NTK theory.
We study the Euler-Lagrange equations for a parameter dependent -invariant Lagrangian on a homogeneous -space. We consider the pullback of the parameter dependent Lagrangian to the Lie group , emphasizing the special invariance properties of the associated Euler-Poincaré equations with advected parameters.
We consider Lagrangian coherent structures (LCSs) as the boundaries of material subsets whose advective evolution is metastable under weak diffusion. For their detection, we first transform the Eulerian advection-diffusion equation to Lagrangian coordinates, in which it takes the form of a time-dependent diffusion or h…
The identification of sources of advection-diffusion transport is based usually on solving complex ill-posed inverse models against the available state- variable data records. However, if there are several sources with different locations and strengths, the data records represent mixtures rather than the separate influ…
Rapid simulations of advection-dominated problems are vital for multiple engineering and geophysical applications. In this paper, we present a long short-term memory neural network to approximate the nonlinear component of the reduced-order model (ROM) of an advection-dominated partial differential equation. This is mo…
We discuss in this note applications of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) to numerical solutions of partial differential equations arising from stochastic models in quantitative finance. In particular, we develop a framework for solving Black-Scholes-type equations by first t…
Paper tackles estimating initial conditions of spatio-temporal processes from sparse data.
DeepMIDE forecasts wind speeds across space, time, and height for offshore wind energy.
Robust PDE method for path-dependent Asian-style options using MPDATA.
Study methods to recover unknown processes in PDEs from data.
Graph neural controlled differential equations learn graph dynamics from vertex observations.
New method uses PINNs to solve complex PDEs with sparse measurements.
Study shows how heat leaks from material sets in low diffusivity scenarios.
Cauchy invariants are now viewed as a powerful tool for investigating the Lagrangian structure of three-dimensional (3D) ideal flow (Frisch & Zheligovsky, Commun. Math. Phys., vol. 326, 2014, pp. 499-505, Podvigina et al., J. Comput. Phys., vol. 306, 2016, pp. 320-342). Looking at such invariants with the modern tools …
We consider the concept of Stokes-Dirac structures in boundary control theory proposed by van der Schaft and Maschke. We introduce Poisson reduction in this context and show how Stokes-Dirac structures can be derived through symmetry reduction from a canonical Dirac structure on the unreduced phase space. In this way, …
New method converts video of dye plumes into PDEs for better understanding.
We study polygonal analogues of several moving boundary problems and their time discretization which preserves the constant area speed property. We establish various polygonal analogues of geometric formulas for moving boundaries and make use of the geometric formulas for our numerical scheme and its analysis of genera…
Investigates fluid flow perturbations using geometric theory.
Modeling wildfire aerosols using satellite data to predict solar radiation reduction.
We propose a method to compute optimal control paths for autonomous vehicles deployed for the purpose of inferring a velocity field. In addition to being advected by the flow, the vehicles are able to effect a fixed relative speed with arbitrary control over direction. It is this direction that is used as the basis for…
The purpose of this paper is to derive the anisotropic averaged Euler equations and to study their geometric and analytic properties. These new equations involve the evolution of a mean velocity field and an advected symmetric tensor that captures the fluctuation effects. Besides the derivation of these equations, the …
INDEQS: A Graph-Based Neural Controlled Differential Equation Framework for Forecasting
New guarantees for uniquely identifying transport maps and vector fields from finite measure-valued data.
USD algorithm transports distributions with or without mass conservation.
We develop an adversarial-reinforcement learning scheme for microswimmers in statistically homogeneous and isotropic turbulent fluid flows, in both two (2D) and three dimensions (3D). We show that this scheme allows microswimmers to find non-trivial paths, which enable them to reach a target on average in less time tha…
A contour integral method recently proposed by Weideman [IMA J. Numer. Anal., to appear] for integrating semi-discrete advection-diffusion PDEs, is extended for application to some of the important equations of mathematical finance. Using estimates for the numerical range of the spatial operator, optimal contour parame…
Study mass transport in low-diffusivity using Lagrangian coordinates.
We introduce a new strategy designed to help physicists discover hidden laws governing dynamical systems. We propose to use machine learning automatic differentiation libraries to develop hybrid numerical models that combine components based on prior physical knowledge with components based on neural networks. In these…
In this manuscript we introduce numerical Gaussian process Kalman filtering (GPKF). Numerical Gaussian processes have recently been developed to simulate spatiotemporal models. The contribution of this paper is to embed numerical Gaussian processes into the recursive Kalman filter equations. This embedding enables us t…
Physics-guided reinforcement learning optimizes swimming in turbulent flows.
We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles used in graph coloring and spectral graph drawing algorithms, examines a measur…
We introduce DeepMoD, a Deep learning based Model Discovery algorithm. DeepMoD discovers the partial differential equation underlying a spatio-temporal data set using sparse regression on a library of possible functions and their derivatives. A neural network approximates the data and constructs the function library, b…
It has been observed that residual networks can be viewed as the explicit Euler discretization of an Ordinary Differential Equation (ODE). This observation motivated the introduction of so-called Neural ODEs, which allow more general discretization schemes with adaptive time stepping. Here, we propose ANODEV2, which is…
New boundary treatment improves accuracy for complex PDEs.
SVGP KAN integrates uncertainty quantification into Kolmogorov-Arnold networks.
FiniteNet uses a neural network to improve PDE solving methods.
Deep learning improves model discovery from sparse sensor data.
This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights in the linear combination is modelled by another linear Gaussian dynamical model…
NOGaP uses neural operators and GPs to solve PDEs with uncertainty quantification.
Survey of diffusion and optimal transport methods in machine learning.
In this paper we propose a new model-based unsupervised learning method, called VarNet, for the solution of partial differential equations (PDEs) using deep neural networks (NNs). Particularly, we propose a novel loss function that relies on the variational (integral) form of PDEs as apposed to their differential form …
A new algorithm computes Wasserstein barycenters without entropic regularization.
Paper extends port-Hamiltonian model to include internal energy for compressible and incompressible flow.
BALLAST optimizes Lagrangian observer placement for ocean vector fields.
Clarifies relation for solving control-affine Schrödinger bridge problems.