Stochastic Differential Equations

Also known as SDE

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21 papers in the last four weeks, up 320% on the four weeks before. 0.1% of all new papers.

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Unbiased and Second-Order-Free Training for High-Dimensional PDEs
May 14, 2026Jaemin Seo, Surin Lee, Jae Yong LeeStochastic Differential Equations Neural PDE Solvers
Department of Artificial Intelligence, Chung-Ang University, Seoul, Republic of Korea.
Variational Inference for Lévy Process-Driven SDEs via Neural Tilting
May 11, 2026Yaman Kindap, Manfred Opper, Benjamin Dupuis +2Stochastic Differential Equations Bayesian Inference
1Imperial College London, UK · 2Technical University of Berlin, Germany · 3INRIA, CNRS, Département d’Informatique de l’Ecole Normale Supérieure / PSL, France
Learning stochastic multiscale models through normalizing flows
May 10, 2026Anan Saha, Arnab GangulyStochastic Differential Equations Multiscale Time-Series Modeling
Department of Mathematics Louisiana State University Baton Rouge, LA 70802
Deterministic Decomposition of Stochastic Generative Dynamics
May 9, 2026Xingyu Song, Yuan Mei, Naoya TakeishiFlow Matching Stochastic Differential Equations
1The University of Tokyo · 2Zhejiang University · *Visiting student at The University of Tokyo from Zhejiang University.
Diffusion-Based Posterior Sampling: A Feynman-Kac Analysis of Bias and Stability
May 7, 2026William Porteous, Advait Parulekar, Sebastien Motsch +2Stochastic Differential Equations Bayesian Inverse Problems
Department of Mathematics, UT Austin. · Department of Electrical and Computer Engineering, UT Austin. · School of Mathematical and Statistical Sciences, Arizona State University.
Variational Smoothing and Inference for SDEs from Sparse Data with Dynamic Neural Flows
May 7, 2026Yu Wang, Arnab GangulyStochastic Differential Equations Bayesian Inference
Department of Mathematics Louisiana State University
Unifying Deep Stochastic Processes for Image Enhancement
May 2, 2026Wojciech Kozłowski, Radosław Kuczbański, Kamil Adamczewski +2Image Enhancement Stochastic Differential Equations
Wrocław University of Science and Technology, Wrocław, Poland · Tooploox, Warsaw, Poland
Structure-Aware Variational Learning of a Class of Generalized Diffusions
Apr 22, 2026Yubin Lu, Xiaofan Li, Chun Liu +2Stochastic Differential Equations
School of Mathematics, South China University of Technology, Guangzhou 510640, China. · Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616 United States · School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332 United States +1
Extraction of informative statistical features in the problem of forecasting time series generated by It{ô}-type processes
Apr 18, 2026Victor Korolev, Mikhail Ivanov, Tatiana Kukanova +4Stochastic Differential Equations Time Series Forecasting
Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics · Moscow Center for Fundamental and Applied Mathematics · Federal Research Center “Computer Science and Control”, Russian Academy of Sciences +2
Diffusion Processes on Implicit Manifolds
Apr 8, 2026Victor Kawasaki-Borruat, Clara Grotehans, Pierre Vandergheynst +1Stochastic Differential Equations Manifold Learning
Signal Processing Laboratory 2 EPFL · Institute of Artificial Intelligence Medical University of Vienna
Score Shocks: The Burgers Equation Structure of Diffusion Generative Models
Apr 8, 2026Krisanu SarkarDiffusion Models Score-Based Generative Modeling
Indian Institute of Technology Bombay, Mumbai, India
Generative Path-Law Jump-Diffusion: Sequential MMD-Gradient Flows and Generalisation Bounds in Marcus-Signature RKHS
Apr 6, 2026Daniel BlochFlow-Based Generative Modeling Stochastic Differential Equations
UNIVERSITY OF PARIS 6 & VINUNIVERSITY · Visting Professor at the College of Engineering and Computer Science, VinUniversity, Hanoi.
Embedded Variational Neural Stochastic Differential Equations for Learning Heterogeneous Dynamics
Apr 1, 2026Sandeep Kumar Samota, Reema Gupta, Snehashish ChakravertyLatent Dynamics Modeling Time Series Forecasting
Department of Mathematics, National Institute of Technology, Rourkela, India · Poverty Alleviation Research Centre, National Institute of Technology, Rourkela, India
Learning noisy phase transition dynamics from stochastic partial differential equations
Mar 31, 2026Luning Sun, Van Hai Nguyen, Shusen Liu +2PDE Surrogate Modeling Phase Transitions
Lawrence Livermore National Laboratory, Livermore, CA, 94550,USA · The University of Texas at Austin, Austin, TX, 78712, USA
Parameter Estimation in Stochastic Differential Equations via Wiener Chaos Expansion and Stochastic Gradient Descent
Mar 27, 2026Francisco Delgado-Vences, José Julián Pavón-Español, Arelly OrnelasParameter Estimation Stochastic Differential Equations
Universitat Autónoma de Barcelona, Departament de Matemàtiques, Edifici C, Facultat de Ciències, 080193, Bellaterra, Spain · Facultad de Ciencias - Universidad Nacional Autónoma de México. Ciudad Universitaria, Ciudad de México, Mexico · Secihti - Centro Interdisciplinario de Ciencias Marinas. IPN., BCS, La Paz, México
Polynomial Speedup in Diffusion Models with the Multilevel Euler-Maruyama Method
Mar 25, 2026Arthur JacotDiffusion Model Inference Acceleration Diffusion Sampling
Neural ODE and SDE Models for Adaptation and Planning in Model-Based Reinforcement Learning
Mar 24, 2026Chao Han, Stefanos Ioannou, Luca Manneschi +4Model-Based RL Latent Dynamics Modeling
School of Computer Science, The University of Sheffield, UK · Cancer Research UK National Biomarker Centre, The University of Manchester, UK · School of Chemical, Materials and Biological Engineering, The University of Sheffield, UK +2
Goal-oriented learning of stochastic differential equations using error bounds on path-space observables
Mar 20, 2026Joanna Zou, Han Cheng Lie, Youssef MarzoukSurrogate Modeling Stochastic Differential Equations
Center for Computational Science & Engineering, Massachusetts Institute of Technology, Cambridge, MA · Department of Mathematics, University of Potsdam, Potsdam, Germany
Symbolic Discovery of Stochastic Differential Equations with Genetic Programming
Mar 10, 2026Sigur de Vries, Sander W. Keemink, Marcel A. J. van GervenStochastic Differential Equations Symbolic Regression
Department of Machine Learning and Neural Computing, Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen, the Netherlands
Stochastic Port-Hamiltonian Neural Networks: Universal Approximation with Passivity Guarantees
Mar 10, 2026Luca Di Persio, Matthias Ehrhardt, Youness OutalebPort-Hamiltonian Systems Hamiltonian Neural Networks
Department of Computer Science - College of Mathematics University of Verona, Strada le Grazie 15 - 37134 Verona, Italy · University of Wuppertal, Chair of Applied and Computational Mathematics, Gaußstrasse 20, 42119 Wuppertal, Germany · Doctoral School in Mathematics, University of Trento Via Sommarive, 14 - 38123 Povo, Italy
Differentiable Stochastic Traffic Dynamics: Physics-Informed Generative Modelling in Transportation
Mar 10, 2026Wuping XinPhysics-Informed Generative Modeling Traffic Flow Estimation
Caliper Corporation
Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems
Mar 9, 2026Gijs van Seeventer, Saber SalehkaleybarStochastic Differential Equations Structural Causal Models
1LIACS, Leiden University, Netherlands
Random Quadratic Form on a Sphere: Synchronization by Common Noise
Mar 6, 2026Maximilian Engel, Anna ShalovaStochastic Differential Equations Dynamical Systems
Korteweg-de Vries Institute for Mathematics, University of Amsterdam · Department of Mathematics and Computer Science, FU Berlin
Lyapunov Stability of Stochastic Vector Optimization: Theory and Numerical Implementation
Mar 4, 2026Thiago Santos, Sebastiao XavierMulti-Objective Optimization Stochastic Differential Equations
Department of Mathematics, Federal University of Ouro Preto, UFOP, Ouro Preto, Brazil
Riemannian Langevin Dynamics: Strong Convergence of Geometric Euler-Maruyama Scheme
Mar 4, 2026Zhiyuan Zhan, Masashi SugiyamaStochastic Differential Equations Langevin Dynamics
The University of Tokyo, Japan · RIKEN Center for AIP, Japan
Neural Diffusion Intensity Models for Point Process Data
Feb 27, 2026Xinlong Du, Harsha Honnappa, Vinayak RaoTemporal Point Processes Variational Inference
Edwardson School of Industrial Engineering, Purdue University · Department of Statistics, Purdue University
Generative Modeling via Kernelized Stochastic Interpolants
Feb 23, 2026Florentin Coeurdoux, Etienne Lempereur, Nathanaël Cuvelle-Magar +2Stochastic Differential Equations Stochastic Interpolants
Capital Fund Management, Paris, France · Département d’informatique, ENS, Université PSL, Paris, France · Collège de France, Paris, France +2
Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Models
Feb 19, 2026Marcos Tapia Costa, Nikolas Kantas, George DeligiannidisStochastic Differential Equations
Department of Mathematics, Imperial College London, UK · Department of Statistics, University of Oxford, UK
Steering Dynamical Regimes of Diffusion Models by Breaking Detailed Balance
Feb 17, 2026Haiqi Lu, Ying TangDiffusion Models Diffusion Sampling
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China · Yingcai Honor College, University of Electronic Science and Technology of China, Chengdu 611731, China · School of Physics, University of Electronic Science and Technology of China, Chengdu 611731, China +2
Drift-Diffusion Matching: Embedding dynamics in latent manifolds of asymmetric neural networks
Feb 16, 2026Ramón Nartallo-Kaluarachchi, Renaud Lambiotte, Alain GorielyRecurrent Neural Networks Dynamical Systems
Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, United Kingdom · Centre for Eudaimonia and Human Flourishing, University of Oxford, 7 Stoke Pl, Oxford, OX3 9BX, United Kingdom · Complexity Science Hub, Metternichgasse 8, Vienna, 1030, Austria

May 14, 2026J/K move · Enter open · S save

Unbiased and Second-Order-Free Training for High-Dimensional PDEs

Jaemin Seo, Surin Lee, Jae Yong Lee

Department of Artificial Intelligence, Chung-Ang University, Seoul, Republic of Korea.

Stochastic Differential Equations Neural PDE Solvers PDE Solving

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Deep learning methods based on backward stochastic differential equations (BSDEs) have emerged as competitive alternatives to physics-informed neural networks (PINNs) for solving high-dimensional partial differential equations (PDEs). By leveraging probabilistic representations, BSDE approaches can avoid the curse of dimensionality and often admit second-order-free training objectives that do not require explicit Hessian evaluations. It has recently been established that the commonly used Euler-Maruyama (EM) time discretization induces an intrinsic bias in BSDE training losses. While high-order schemes such as Heun can fully eliminate this bias, such schemes re-introduce second-order spatial derivatives and incur substantial computational overhead. In this work, we provide a principled analysis of EM-induced loss bias and propose an unbiased, second-order-free training framework that preserves the computational advantages of BSDE methods. Our code is available at https://github.com/seojaemin22/Un-EM-BSDE.