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.
Study natural invariants for third order nonlinear operators on 2D manifolds.
Study natural invariants for differential operators, simplifying their equivalence problem.
This note introduces a regression technique for finding a class of nonlinear integro-differential operators from data. The method parametrizes the spatial operator with neural networks and Fourier transforms such that it can fit a class of nonlinear operators without needing a library of a priori selected operators. We…
The paper studies boundedness of pseudo-differential operators on smooth manifolds.
Unified bounds for neural networks incorporating physical laws.
Paper quantifies neural operators' efficiency for solving nonlinear parabolic PDEs.
Bayesian model learns physics laws from data with uncertainty quantification.
Kernel method approximates Koopman operator eigenfunctions.
Uniform estimates for complex equations on compact manifolds found.
New method deflates manifolds to visualize high-dimensional data.
Bayesian methods solve complex nonlinear PDEs efficiently.
Study generalizes Picard iteration for nonlinear PDEs, deriving bounds on error.
In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two objectives at the same time: to accurately predict dynamics of complex systems and to …
We give an explicit formula, as a formal differential operator, for quantum microformal morphisms of (super)manifolds that we introduced earlier. Such quantum microformal morphisms are essentially oscillatory integral operators or Fourier integral operators of a particular kind. They act on oscillatory wave functions, …
Study solves optimal portfolio selection using HJB equation.
New method identifies key genes affecting phenotypes in biological systems.
New Spencer complexes for Lie groupoids developed.
While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear continuous operator. This universal approximation theorem is suggestive of the pot…
In this paper, we consider nonlinear PDEs in a port-Hamiltonian setting based on an underlying jet-bundle structure. We restrict ourselves to systems with 1-dimensional spatial domain and 2nd-order Hamiltonian including certain dissipation models that can be incorporated in the port- Hamiltonian framework by means of a…
We prove certain localized and global differential Harnack inequality for all positive solutions to the geometric conjugate heat equation coupled to the forward in time Ricci flow. In this case, the diffusion operator is perturbed with the curvature operator, precisely, the Laplace-Beltrami operator is replaced with "$…
Paper introduces a method for operator learning using random features.
This paper lays the foundations for a nonlinear theory of differential geometry that is developed in a subsequent paper which is based on Colombeau algebras of tensor distributions on manifolds. We adopt a new approach and construct a global theory of algebras of generalised functions on manifolds based on the concept …
Proposes a new method to learn operators for stochastic problems using DeepONet with autoencoder.
Fundamental solutions found for PDEs in Finsler geometry.
Neural operators correct PDE residuals to improve BIP solutions.
Study shows neural operators can efficiently solve complex reaction-diffusion systems.
We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray transforms of lower order coefficients. We also give two different boundary determinat…
In this paper we present nonparametric estimators for coefficients in stochastic differential equation if the data are described by independent, identically distributed random variables. The problem is formulated as a nonlinear ill-posed operator equation with a deterministic forward operator described by the Fokker-Pl…
We propose a new method to solve eigenvalue problems for linear and semilinear second order differential operators in high dimensions based on deep neural networks. The eigenvalue problem is reformulated as a fixed point problem of the semigroup flow induced by the operator, whose solution can be represented by Feynman…
Interdisciplinary study linking potential theory and elliptic PDEs.
Attention augments forest for tabular data accuracy.
New machine learning methods solve complex PDEs with improved accuracy.
Study on existence of metrics in conformal geometry with constraints on Schouten tensor.
Infinitesimal variation of Action functional in classical (non-quantum) field theory with higher derivatives is presented in terms of well-defined intrinsic geometric objects independent of the particular field which varies. 'Integration by parts' procedure for this variation is then described in purely formal language…
This article provides a version of scale calculus geared towards a notion of (nonlinear) Fredholm maps between certain types of Frechet spaces, retaining as many as possible of the properties Fredholm maps between Banach spaces enjoy, and the existence of a constant rank theorem for such maps. It does so by extending t…
Constructs differential characters on nonlinear Graßmannians.
The new business paradigms originate a strong necessity to re-think the theory of the firm with the aim to get a better understanding on the organizational and functional principles of the firm, operating in the investment economies in the prosperous societies. In this connection, we make the innovative research to adv…
We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes, by construction, are designed to deal with cases where: (1) all we observe are …
Develops a framework for learning nonlinear operators using Mercer kernels.
Scalable Gaussian Process Operator tackles high-dimensional PDEs.
We establish a microscopic convexity principle for nonlinear elliptic and parabolic partial differential equations in general form.
Estimates for polynomial operators using determinant majorization and subharmonics.
Physics-informed WNO learns PDE solutions without labeled data.
Recently, the infinitesimal moduli space of heterotic compactifications was described in supergravity and related to the cohomology of a target space differential. In this paper we identify the marginal deformations of the corresponding heterotic nonlinear sigma model with cohomology classes of a worldsheet BRST …
This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art model reduction methods that are intrusive and thus require full knowledge of t…
The paper tackles data-driven optimal control of unknown nonlinear systems using RKHS.
Paper develops a novel approach for optimal control using kernel methods.
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In particular, we introduce \emph{hidden physics models}, which are essentially data-efficien…