arXiv research

Eikonal-Constrained QRL improves goal-reaching in reinforcement learning.

In this study, we give definitions and characterizations of eikonal slant helix curves, eikonal Darboux helices and non-normed eikonal Darboux helices in three dimensional Riemannian manifold 3 M . We show that every eikonal slant helix is also an eikonal Darboux helix. Furthermore, we obtain that if the curve a is a n…

In this study, we give definitions and characterizations of eikonal slant helices, eikonal Darboux helices and non-normed eikonal Darboux helices in 3-dimensional pseudo- Riemannian manifold M . We show that every eikonal slant helix is also an eikonal Darboux helix for timelike and spacelike curves. Furthermore, we ob…

In this paper, we define the notion of eikonal helix and eikonal slant helix for null curves in the 4-dimensional Lorentzian manifold M 1 4 and give a characterization for the null curve to be the null eikonal helix. Moreover, we indicate an important relation between the null eikonal helix and null eikonal slant helix…

In this paper, we define f-eikonal helix curves and f-eikonal V_{n}-slant helix curves in a n-dimensional Riemannian manifold. Also, we give the definition of harmonic curvature functions related to f-eikonal helix curves and f-eikonal V_{n}-slant helix curves in a n-dimensional Riemannian manifold. Moreover, we give c…

Let M{\subset}\mathbb{R}^{n} be a Riemannian helix submanifold with respect to the unit direction d{\in}\mathbb{R}^{n} and f:M{\to}\mathbb{R} be a eikonal function. We say that M is a f-eikonal helix submanifold if for each q{\in}M the angle between {\nabla}f and d is constant.Let M{\subset}\mathbb{R}^{n} be a Riemanni…

Estimating boundaries from point clouds with improved accuracy and rigorous error estimates.

In this paper, we define a new kind of slant helix called f-eikonal V_{n}-slant helix in Pseudo- Riemannian manifolds and give the definition of harmonic curvature functions related to the f-eikonal V_{n}-slant helix in Pseudo- Riemannian manifolds. Moreover, we give some characterizations of f-eikonal V_{n}-slant heli…

Unified framework solves nonlinear PDEs and IPs using Gaussian processes.

In this paper, we prove that a quartic polynomial solution of the eikonal equation $|\nabla_x f|^2=16x^{6}$ in $\R{n}$ is either an isoparametric polynomial or congruent to a polynomial $f=(\sum_{i=1}^n x_i^2)^2-8(\sum_{i=1}^k x_i^2)(\sum_{i=k+1}^{n} x_i^2)$, $k=0,1,\...,[\frac{n}{2}]$.

This work proposes a model for geodesic distances and flows on manifolds.

EikoNet uses deep learning to solve the Eikonal equation quickly and efficiently.

A new depth measure based on optimal control theory captures multi-modal data.

Researchers use operator learning to predict cardiac activation and repolarization times.

A normal form for edge metrics is derived under the necessary conditions that the metric be normalized and exact. The normal forms for such an edge metric are shown to be in 1-1 correspondence with representative metrics for a reduced conformal infinity on the boundary. The normal form is constructed via solution of a …

Given a warped product of the real line with a Riemannian manifold of arbitrary dimension, we classify the hypersurfaces whose tangent spaces make a constant angle with the vector field tangent to the real direction. We show that this is a natural setting in which to extend previous results in this direction made by se…

Making use of the Kerr theorem for shear-free null congruences and of Newman's representation for a virtual charge ``moving'' in complex space-time, we obtain an axisymmetric time-dependent generalization of the Kerr congruence, with a singular ring uniformly contracting to a point and expanding then to infinity. Elect…

Given a vector field $X$ in a Riemannian manifold, a hypersurface is said to have a canonical principal direction relative to $X$ if the projection of $X$ onto the tangent space of the hypersurface gives a principal direction. We give different ways for building these hypersurfaces, as well as a number of useful charac…

A new method infers parameters from PDEs using Gaussian processes.

Neural-PDE learns PDEs from data using LSTM, outperforming traditional methods.

Neural Q-learning tackles high-dimensional PDEs.

Partial differential equations (PDEs) are commonly derived based on empirical observations. However, recent advances of technology enable us to collect and store massive amount of data, which offers new opportunities for data-driven discovery of PDEs. In this paper, we propose a new deep neural network, called PDE-Net …

PDE-DKL combines NNs and GPs for high-dimensional PDE problems.

Solves second-order PDEs using quotients and differential invariants.

PRISMA uses PDE residuals for fast, robust, and accurate inference.

Meta-learning base distributions for efficient PDE solutions.

Researchers prove a 30-year-old cosmological conjecture about spacetime.

Kernel method learns PDEs from noisy data.

Solves a PDE for Landsberg surfaces using new Finsler surface insights.

Survey on conservation laws for geometric PDEs.

Using the theory of the symmetry group for PDEs [15, 17], we derive the symmetry group G associated to surfaces PDE. Several group invariant solutions of the surfaces PDE are given by solving a reduced system of partial differential equations.

PDE-based G-CNNs add geometric symmetries to CNNs without augmentation.

Develops arithmetic PDE geometry concepts like curvature and cohomology.

The cost of belief changes with precision and is a hyperbolic geometry.

The paper presents a PDE method for xVA incorporation in financial derivatives.

New PDEs of mixed type emerge in fluid mechanics and geometry.

PDE-NetGen converts physical equations to neural networks for various scientific problems.

Automated PDE discovery from multiple noisy experiments.

Improved neural PDEs trained on augmented data enhance model accuracy and efficiency.

In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving this goal, major challenges remain to be resolved, including learning PDE under …

Meta-learning neural networks to solve diverse PDEs efficiently.

It is shown that the characteristic vector field associated to a first order PDE has the same form of an infinitesimal generator of an odd-symplectic transformation with contact Hamiltonian the given PDE. It is considered under which condition such PDE has a characteristic vector field commuting with a generator of an …

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 …

New formula for portfolio risk management using conditional PDEs.

We consider the problem of computing the integrable sub-distributions of the non-integrable Vessiot distribution of multi-dimensional second order partial differential equations (PDEs). We use Vessiot theory and solvable structures to find the largest integrable distributions contained in the Vessiot distribution assoc…

Novel neural network solves PDEs with multi-scale resolution.

Error estimates for nonlinear PDEs using kernel/GP methods.

Adapts PDE method to prove $L^\infty$ estimates for complex Hessian equations.