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# Stochastic Differential Equations

5 related articles

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  1. arXiv

    Bifidelity material models get a posterior, not just a fit: a sampling hypernetwork runs Langevin trajectories over network weights

    Bifidelity modeling uses cheap low-fidelity simulations to supplement scarce high-fidelity experiments, but the usual product is a single deterministic fit that says little about how trustworthy a prediction is. This work extends a single-fidelity Langevin sampling hypernetwork to bifidelity data, using a shared-latent data model that predicts both the low-fidelity response and the high-fidelity correction while a learned drift network generates parameter samples from the posterior score. On a synthetic hyperelastic case, conditional staged training cut the SPD-drift RMSE from 0.075 to 0.024 and the convex-potential drift from 0.081 to 0.017; on experimental and DNS data, predicting the high-fidelity response directly gave lower error than an additive discrepancy.

    Reese E. Jones（First author）
    Langevin Sampling HypernetworkMultifidelity ModelingUncertainty QuantificationHypernetworkStochastic Differential Equations
  2. arXiv

    TORNADO lets PDE ensemble forecasts vary their noise by state, cutting calibration error roughly 2x to over 5x versus representative baselines at five network evaluations

    Probabilistic PDE surrogates often turn overconfident in few-step inference, producing predictive spreads narrower than the real uncertainty. TORNADO recasts next-step prediction as stochastic transport between the variational-autoencoder posteriors of consecutive frames, and lets a neural network set the diffusion amplitude from the latent state instead of a fixed global noise schedule. On four synthetic PDE datasets, at a fixed budget of five network evaluations, it reaches the lowest calibration error, roughly 2x to over 5x lower than representative baselines, while keeping comparable predictive accuracy.

    Jorge Mifsut Benet（First author）
    TORNADOProbabilistic PDE ForecastingState-Dependent DiffusionUncertainty CalibrationStochastic Differential Equations
  3. arXiv

    KC-maps drops trajectory data: learning a transition kernel from drift and diffusion lets peptide sampling outrun classical MD

    KC-maps learns the finite-time transition kernel of a stochastic differential equation directly as a neural network map, trained only on uncorrelated marginal samples plus the known drift and diffusion coefficients rather than on paired simulated trajectories. Boundary conditions are built into the network architecture, and a training objective derived from the Kolmogorov–Chapman equation keeps transitions composed over different time scales consistent in distribution. On alanine dipeptide, tetrapeptide and hexapeptide it replaces up to 70 fs of sequential integration with a single learned transition, reaches lower TICA-2 distances at matched GPU-hour budgets, and on AL6 covers conformational modes absent from the training data.

    Majdi Hassan（First author）
    Kolmogorov-Chapman MapsNormalizing FlowStochastic Differential EquationsMolecular Dynamics
  4. arXiv

    Instrumental variables move into continuous time: as confounding grows, discrete-time estimators drift while path-based moments hold

    Continuous-time stochastic processes had no instrumental-variable framework, and discrete-time methods place the structural sparsity on finite-step transitions rather than on the actual mechanism. The work writes relevance, exclusion and exogeneity directly at the infinitesimal level of a stochastic differential equation's drift and builds moment conditions from the whole instrument path, giving an identification condition and a consistent estimator in the linear case. On confounded Ornstein-Uhlenbeck simulations, maximum likelihood becomes systematically biased as confounding grows while this estimator stays stable, and a single instrument process identifies multi-dimensional effects.

    Lars Pennig（First author）
    Instrumental Variable AnalysisStochastic Differential EquationsCausal Effect EstimationIVSDE
  5. arXiv

    SGD convergence rates can be transferred: one Lyapunov calculation on a diffusion, then carried back window by window

    Finite-time convergence bounds for stochastic gradient algorithms can be transferred from Lyapunov estimates for an associated stochastic differential equation, recovering known rates for strongly convex SGD and stochastic Heavy Ball.

    Durham University
    Neil Walton（First author, Corresponding author）
    Rate Transfer via SDE Lyapunov AnalysisStochastic Gradient DescentStochastic Differential EquationsStochastic ApproximationStochastic Heavy Ball

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