Stochastic Differential Equations

Also known as SDE

Stochastic differential equations (SDEs) describe how systems evolve continuously under both drift and random fluctuations, modeling distributions of possible paths rather than a single forecast. Approaches include numerical solvers such as Euler–Maruyama, Fokker–Planck and backward-SDE methods, and neural SDEs, score models, and operator learners that infer dynamics or generate trajectories from data. Applications range from diffusion-based image generation and irregular clinical or financial time series to weather, physical simulation, molecular dynamics, and stochastic control. A central challenge is making simulation and inference efficient while handling sparse observations, constraints, jumps, or heavy tails; flexible learned models still face open questions about identifiability, stability, and guarantees beyond benchmark settings.

Latest papers

114 papers19 papers in the last four weeks, up 12% on the four weeks before. 0.1% of all new papers.

Identifiable Signed Causal Learning via Latent Stochastic Differential Equations for Inferring Brain Dynamic Effective Connectivity
Nov 2, 2026Yiding Wang, Chen QiaoCausal Discovery Causal Structure Learning
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049 P.R. China.
Learning hidden-state dynamics from unpaired snapshots with lift-project SDEs
Oct 31, 2026Qi Wang, Uduak George, Gustaaf JacobsLatent Dynamics Modeling Stochastic Differential Equations
Department of Aerospace Engineering, San Diego State University, San Diego, CA, USA · Department of Mathematics and Statistics, San Diego State University, San Diego, CA, USA
Conditional Neural SDEs for Financial Time-Series Generation
Oct 30, 2026Sina Molavipour, Alireza M. Javid, Björn Löfdahl +1Time Series Generation Stochastic Differential Equations
Generative SDEs with Trainable Diffusion and Density-Based Losses
Oct 30, 2026Angxiu NiGenerative Modeling Stochastic Differential Equations
Department of Mathematics, University of California, Irvine, USA
Displacement Moments and Path-Terminal Separation in Brownian Interpolant Sampling
Oct 27, 2026Zhong HanStochastic Interpolants Stochastic Differential Equations
Department of Biomedical Engineering, College of Design and Engineering, National University of Singapore
Holomorphic Cauchy Networks for Efficient Stationary Tail Computation in High-Dimensional Reflected Brownian Motions
Oct 27, 2026Kehan WangComplex-Valued Neural Networks Stochastic Differential Equations
School of Data Science, The Chinese University of Hong Kong, Shenzhen, China
ZENO: Nonlinear filtering with Zakai Equation Neural Operators
Oct 23, 2026Aaditya Prasad, Steven W. Flavell, Brian DePasqualeLatent Dynamics Modeling Stochastic Differential Equations
Picower Institute for Learning & Memory, Department of Brain & Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA · Howard Hughes Medical Institute, Picower Institute for Learning & Memory, Department of Brain & Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA · Department of Biomedical Engineering, Boston University, Boston, MA 02215, USA
Identifiability from Stationary Covariance in Linear SDEs with Reciprocal Interactions and Latent Variables
Oct 22, 2026Ana Leticia Garcez Vicente, Saber SalehkaleybarCausal Identifiability Stochastic Differential Equations
Leiden Institute of Advanced Computer Science (LIACS), Leiden University, Netherlands
Continuous-depth Deep Gaussian Processes
Oct 22, 2026Ying Li, Sanyou Wu, Zi Yang +6Deep Gaussian Processes Gaussian Process Regression
National University of Singapore · Columbia University · The University of Hong Kong +3
Improved Training of Strong Stochastic Flow Maps
Oct 21, 2026Zander W. Blasingame, Antonio Franca, Raul Minan +3Flow Map Learning Stochastic Differential Equations
AITHYRA · Technische Universität Wien · Technische Universität München +1
Deep Pontryagin Learning for Continuous-Time Stochastic Control with Jumps
Oct 19, 2026Jean-Loup Dupret, Patrick CheriditoStochastic Optimal Control Policy Learning
Department of Mathematics and RiskLab, ETH Zurich, Rämistrasse 101, Zurich, 8092, Switzerland
StochLOB: Heavy-Tailed Score Matching for Robust Limit Order Book Trend Prediction
Oct 15, 2026Arshia Abolghasemi, Seyed Reza Tavakoli, Parsa Naderi +7Limit Order Book Forecasting Score Matching
Dataism Laboratory for Quantitative Finance · Sharif University of Technology · Amirkabir University of Technology +3
From Global to Tail Convergence: Dynamics of $α$ -Stable Score-Based Generative Models
Oct 14, 2026Ianis Hammani, Claire BoyerScore-Based Generative Modeling Diffusion Models
ENS Paris Saclay, LMO · LMO, IUF
Wong--Zakai Convergence and FNO Learning for Stochastic Volterra Equations
Oct 13, 2026Wonjae Lee, Jiuk Jang, Hyungbin ParkNeural Operators Fourier Neural Operator
InnoCore AI Meta-Scientist Research Group, KAIST, Daejeon 34141, South Korea. · Department of Mathematical Sciences, Seoul National University, Seoul 08826, South Korea. · Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, 1, Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea.
Broadly Applicable Approximate MCMC for Switching Stochastic Differential Equations Using Uniformization and Time-Conditioned Factorized Neural Likelihood Estimation
Oct 7, 2026Shion Hosoda, Michiaki HamadaStochastic Differential Equations Regime-Switching Dynamical Systems
Waseda University · National Institute of Advanced Industrial Science and Technology · Nippon Medical School
Boundary-aware Reinforcement Learning for Hypercube State Spaces via Deterministic Policy Gradient
Oct 7, 2026Lijun Bo, Yijie Huang, Chenhao LuRL Control Reinforcement Learning
School of Mathematics and Statistics, Xidian University, Xi’an, 710126, China · Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China · School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China
Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models
Oct 6, 2026Yuzhen Zhao, Yating Liu, Quentin GuibertStochastic Differential Equations Conditional Distribution Estimation
CEREMADE, CNRS, Universite Paris-Dauphine, PSL, 75016 Paris, France
HyperNSDE: Personalized Neural SDEs for Joint Static-Longitudinal Clinical Data Generation
Oct 5, 2026Perrine Chassat, Agathe GuillouxStochastic Differential Equations Synthetic Data Generation
Inria, Université Paris Cité, Inserm, HeKA F-75015 Paris, France
Sharp dimensional analysis of midpoint methods for Langevin sampling
Oct 5, 2026Fan Chen, Sinho Chewi, Jianfeng Lu +1Markov Chain Monte Carlo Stochastic Differential Equations
Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology. · Department of Statistics and Data Science, Yale University. · Department of Mathematics, Duke University. +1
Langevin Flow Maps: Efficient Molecular Dynamics and Transition Path Sampling
Oct 5, 2026Sam McCallum, Niklas Rindtorff, Alexander Tong +1Stochastic Differential Equations Machine Learning Interatomic Potentials
University of Bath · AITHYRA
Gaussian Flow Dynamics: Simulation-Free Neural SDE Learning Beyond One-Time Marginals
Oct 3, 2026Grigory Bartosh, Christian A. NaessethStochastic Differential Equations Latent Dynamics Modeling
Informatics Institute University of Amsterdam
Probability flow ODEs in score-based and reflected diffusion models
Oct 2, 2026Rama CONTDiffusion Sampling Diffusion Models
Mathematical Institute, University of Oxford
SDECast: Probabilistic Weather Forecasting in Continuous Time with Neural SDEs
Oct 2, 2026Maria Marchenko, Martin Andrae, Fredrik Lindsten +1Weather Forecasting Probabilistic Forecasting
Linköping University, Sweden
Adaptive Second-Order Solvers for Fast Stochastic Diffusion Sampling
Oct 2, 2026Ella Kemperman, Luca AmbrogioniDiffusion Sampling Diffusion Timestep Scheduling
Radboud University
Tangent Schrödinger Bridge Matching: Learning Stochastic Transport with Mechanistic Sensitivities
Oct 2, 2026Jowaria Khan, Elizabeth Bondi-KellySchrödinger Bridges Optimal Transport
University of Michigan
Inference for stochastic differential equations driven by weighted sub-fractional Brownian motion using neural networks and the Euler approximation
Sep 30, 2026J. H. Ramirez-GonzalezParameter Estimation Stochastic Differential Equations
Institute of Mathematics and Statistics, University of São Paulo (IME–USP), São Paulo, Brazil
Learning Continuous Neural Representation of Stochastic Hybrid Systems
Sep 30, 2026Sangli Teng, Hang Liu, Koushil SreenathDynamical Systems Stochastic Differential Equations
Unified Optimality Conditions for Stochastic Optimal Control in the Rough Path and Itô Frameworks
Sep 29, 2026Thomas LewStochastic Differential Equations Stochastic Optimal Control
Toyota Research Institute
Identifiability Guarantees for Drivers and Dynamics of Delayed Physical Systems
Sep 29, 2026Julien Boussard, Antoine Debouchage, Théo SaulusStochastic Differential Equations Causal Identifiability
School of Computer Science, McGill University, Canada · Mila - Quebec AI Institute, Canada · LaMMe, Université Évry Paris-Saclay, France +1
Structured Neural SDEs for Functional Calibration
Sep 28, 2026Francesco Piatti, Andrea Iannucci, Thomas CassStochastic Differential Equations
Department of Mathematics, Imperial College London

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Identifiable Signed Causal Learning via Latent Stochastic Differential Equations for Inferring Brain Dynamic Effective Connectivity

Yiding Wang, Chen Qiao

School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049 P.R. China.

Causal Discovery Causal Structure Learning Brain Network Analysis Causal Identifiability Stochastic Differential Equations

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Understanding how brain regions interact to support cognitive tasks requires characterizing directed causal influences among them, known as effective connectivity (EC). As inter-regional coupling changes over time, a dynamic EC (dEC) estimate is required to track this temporal variation. Existing dEC learning methods typically lack a causal rationality guarantee or an identifiability analysis, and output unsigned connectivity that cannot distinguish excitatory from inhibitory influences, which limits further study of brain mechanisms. We propose ISCL, a latent stochastic differential equation framework that derives dEC from latent dynamics through a causal influence operator defined in observation space. As established by a rationality theorem, the operator captures a directed interventional response at each brain state, and under invariance assumptions the operator is identifiable from data, with its signed output separating excitatory from inhibitory influences. On synthetic benchmarks, \model recovers the causal structure on Lorenz96 and achieves the lowest mean structural Hamming distance among compared methods on NetSim, while preserving signed influence structures that distinguish excitatory from inhibitory interactions. Applied to HCP Social Cognition task-fMRI, ISCL reveals a signed architecture whose stability across seeds supports the identifiability guarantee, identifies dominant source and target networks consistent with social-cognition systems, and shows that condition-specific training strengthens causal outflow from the default-mode and frontoparietal networks during theory-of-mind processing. In this task, the recovered signed structure reveals network-level excitatory and inhibitory organization, with the dorsal-attention network as the only consistently positive out-strength source.