Papers Numerical Integration
“Numerical Integration” 태그가 달린 논문 242편 · 필터 해제
Gaussian Processes and Reproducing Kernels: Connections and Equivalences
This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). T…
Gaussian ProcessesNumerical IntegrationFast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models
Diffusion probabilistic models generate samples by learning to reverse a noise-injection process that transforms data into noise. Reformulating this reverse process as a deterministic probability flow ordinary differenti…
Numerical IntegrationHow Far Are We from Optimal Reasoning Efficiency?
Large Reasoning Models (LRMs) demonstrate remarkable problem-solving capabilities through extended Chain-of-Thought (CoT) reasoning but often produce excessively verbose and redundant reasoning traces. This inefficiency …
16kBenchmarkingNumerical IntegrationODE-GS: Latent ODEs for Dynamic Scene Extrapolation with 3D Gaussian Splatting
We present ODE-GS, a novel method that unifies 3D Gaussian Splatting with latent neural ordinary differential equations (ODEs) to forecast dynamic 3D scenes far beyond the time span seen during training. Existing neural …
3DGSNeRFNeural RenderingNumerical IntegrationOperator-Splitting Methods for Neuromorphic Circuit Simulation
A novel splitting algorithm is proposed for the numerical simulation of neuromorphic circuits. The algorithm is grounded in the operator-theoretic concept of monotonicity, which bears both physical and algorithmic signif…
Numerical IntegrationArtificial Intelligence for Direct Prediction of Molecular Dynamics Across Chemical Space
Molecular dynamics (MD) is a powerful tool for exploring the behavior of atomistic systems, but its reliance on sequential numerical integration limits simulation efficiency. We present MDtrajNet-1, a foundational AI mod…
Numerical IntegrationContinuous-time iterative linear-quadratic regulator
We present a continuous-time equivalent to the well-known iterative linear-quadratic algorithm including an implementation of a backtracking line-search policy and a novel regularization approach based on the necessary c…
Numerical IntegrationDiscretization of Linear Systems using the Matrix Exponential
Discretizing continuous-time linear systems typically requires numerical integration. This document presents a convenient method for discretizing the dynamics, input, and process noise state-space matrices of a continuou…
Numerical IntegrationA Dictionary of Closed-Form Kernel Mean Embeddings
Kernel mean embeddings -- integrals of a kernel with respect to a probability distribution -- are essential in Bayesian quadrature, but also widely used in other computational tools for numerical integration or for stati…
FormNumerical IntegrationOn the Eigenvalue Tracking of Large-Scale Systems
The paper focuses on the problem of tracking eigenvalue trajectories in large-scale power system models as system parameters vary. A continuation-based formulation is presented for tracing any single eigenvalue of intere…
Numerical IntegrationAsian Basket Spread Options: A New Approximation Based on Stochastic Taylor Expansions
We present closed analytical approximations for the pricing of Asian basket spread options under the Black-Scholes model. The formulae are obtained by using a stochastic Taylor expansion around a log-normal proxy model a…
Numerical IntegrationRiemannian Patch Assignment Gradient Flows
This paper introduces patch assignment flows for metric data labeling on graphs. Labelings are determined by regularizing initial local labelings through the dynamic interaction of both labels and label assignments acros…
Numerical IntegrationUncertainty QuantificationNeural network-enhanced integrators for simulating ordinary differential equations
Numerous applications necessitate the computation of numerical solutions to differential equations across a wide range of initial conditions and system parameters, which feeds the demand for efficient yet accurate numeri…
Computational EfficiencyNumerical IntegrationForce-Free Molecular Dynamics Through Autoregressive Equivariant Networks
Molecular dynamics (MD) simulations play a crucial role in scientific research. Yet their computational cost often limits the timescales and system sizes that can be explored. Most data-driven efforts have been focused o…
Numerical IntegrationComputing Modes of Instability of Parameterized Nonlinear Systems for Vulnerability Assessment
Engineered systems naturally experience large disturbances that can disrupt desired operation because the system may fail to recover to a stable equilibrium point. It is valuable to determine the mechanism of instability…
Numerical IntegrationVulnerability DetectionPI-Controlled Variable Time-Step Power System Simulation Using an Adaptive Order Differential Transformation Method
Dynamic simulation plays a crucial role in power system transient stability analysis, but traditional numerical integration-based methods are time-consuming due to the small time step sizes. Other semi-analytical solutio…
Computational EfficiencyNumerical IntegrationDenoising Hamiltonian Network for Physical Reasoning
Machine learning frameworks for physical problems must capture and enforce physical constraints that preserve the structure of dynamical systems. Many existing approaches achieve this by integrating physical operators in…
DenoisingNumerical IntegrationUnderdamped Diffusion Bridges with Applications to Sampling
We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate dif…
Numerical IntegrationProvable Quantum Algorithm Advantage for Gaussian Process Quadrature
The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors …
Gaussian ProcessesNumerical IntegrationEFiGP: Eigen-Fourier Physics-Informed Gaussian Process for Inference of Dynamic Systems
Parameter estimation and trajectory reconstruction for data-driven dynamical systems governed by ordinary differential equations (ODEs) are essential tasks in fields such as biology, engineering, and physics. These inver…
Computational EfficiencyDenoisingNumerical Integrationparameter estimation+1