The Stochastic Computation workshop highlights recent advances at the intersection of stochastic processes and numerical analysis. Core topics include:
– the design and analysis of algorithms for stochastic differential equations (SDEs and SPDEs);
– theoretical insights and practical advances in accelerated Markov chain Monte Carlo (MCMC) methods; and,
– emerging directions such as rough path theory, uncertainty quantification for random PDEs, backward SDEs (BSDEs), and stochastic optimization techniques used in machine learning (e.g., stochastic gradient descent).
We anticipate strong synergies with the Foundations of Data Science and Machine Learning and Geometric Integration and Computational Mechanics workshops. In particular, the rapidly evolving field of diffusion-based generative modeling presents an exciting new frontier, blending ideas from stochastic numerics, high-dimensional sampling, and machine learning. These connections promise rich opportunities for cross-pollination, especially in the development of new structure-preserving algorithms and scalable inference techniques with rigorous mathematical foundations. The extent of interaction will naturally depend on the participants and confirmed speakers.
Organizers
INRIA
Rutgers University Flatiron Institute
Chalmers University of Technology
Speakers
Semi-plenary speakers
Université de Pau et des Pays de l’Adour
University of Bonn
Invited speakers
Stanford University
Chalmers University of Technology & University of Gothenburg
TU Wien
TU Berlin
University of Klagenfurt
École des Ponts ParisTech
TU Delft & KTH Royal Institute of Technology
University of Edinburgh
University of Augsburg
Duke University
Radboud University
Université de Lorraine
LaMME
Université Gustave Eiffel
University of Mannheim
Imperial College London
University of Passau
Central South University
New York University
Yale University
Monday, 13 July
![[HS 13 – 2nd Floor]](https://focm2026.univie.ac.at/wp-content/uploads/2026/06/HS13.png){kind=link}
14:00-15:00 semi-plenary talk
Charles-Edouard Bréhier (Université de Pau et des Pays de l’Adour)
I will first present a positivity preserving splitting scheme for some nonlinear stochastic heat equations driven by multiplicative space-time white noise in dimension 1, which converge with strong rate 1/4.
Second, I will show how similar techniques can be used to design domain preserving schemes for finite dimensional systems of stochastic differential equations: I will present a general class of integrators of strong order 1/2 and weak order 1. I will also present an integrator of strong order 1 for systems driven by one-dimensional noise, in the spirit of the Milstein scheme.
Finally, I will show how splitting domain preserving schemes can be obtained for a generalized version of the stochastic Nagumo equation.
This talk is based on joint works with David Cohen, Gijs Custers and Johan Ulander.
15:00-15:30
Gabriel Lord (Radboud University)
We consider a one-dimensional SDE with linear multiplicative noise from fractional Brownian motion fBM). The fBM is parametrized by $H\in(0,1)$ the Hurst parameter and we interpret the integral as a WIS integral which allows us to understand the SDE for all values of $H$. We will introduce fBM and some of the theory needed to understand the WIS integral such as the Wick product [Mishura]. We will consider the numerical approximation proposed in [Mishura], propose some modifications and indicate how the method may be implemented.
15:30-16:00
Ben Leimkuhler (University of Edinburgh)
I will discuss the design of Langevin-based sampling algorithms which vary parameters like friction or timestep. While many ad-hoc schemes are in use for this purpose, it is desirable to find methods with reliable properties in terms of their evolving or stationary measures. These approaches can also motivate the development of stable optimization schemes. I will discuss the practical uses of these schemes including applications in machine learning. I will also discuss some alternatives for on-the-fly preconditioning.
16:00-16:30 Coffee Break
16:30-17:00
Sara Mazzonetto (Université de Lorraine)
We consider a class of one-dimensional diffusion processes whose dynamics are perturbed by the presence of a point interface. Such an interface may be partially reflective, corresponding to skew diffusion, or sticky, corresponding to a diffusion that spends positive time at the interface. The behavior of the process is characterized by skewness and stickiness parameters. In this talk, we focus on the sticky case. We describe these processes and their main properties, with the aim of studying discrete approximations of their local time. In particular, we discuss rates of convergence and limiting distributions for these approximations. We also investigate how local-time approximation affects the estimation of the stickiness parameter when a single trajectory of the process is observed at discrete times. This talk is partially based on joint work with A. Anagnostakis.
17:00-17:30
Daniel Rudolf (University of Passau)
Gibbsian polar slice sampling, a Markov chain Monte Carlo method for approximate sampling of distributions only known up to normalizing constants, is able to perform well in high-dimensional settings and heavy-tailed scenarios. The aim of the presentation is to provide an introduction to the sampling scheme as well as to point to recent theoretical developments. Specifically, we show dimension-robust spectral gap estimates of the corresponding Markov operator which yield, under appropriate assumptions, dimension-independent convergence guarantees.
17:30-18:00
Xiaojie Wang (Central South University)
Sampling from a high-dimensional probability distribution is a fundamental algorithmic task arising in wide-ranging applications across multiple disciplines, including scientific computing, computational statistics and machine learning. This talk will focus on high-dimensional sampling algorithms based on several time discretizations of stochastic differential equations (SDEs). New algorithms and new error bounds will be provided to accelerate the sampling in non-convex settings, where the convergence rates and the dimension dependence are explicitly revealed. Numerical experiments will be presented to corroborate the theoretical findings.
18:00-18:30
Grigorios Pavliotis (Imperial College London)
Tuesday, 14 July
14:00-14:30
Benjamin Gess (TU Berlin)
We begin by informally demonstrating how the gradient flow structure of the deterministic thin film equation, which encodes the balance between driving capillary forces and limiting viscous forces, can be used as a foundation for the thermodynamically consistent introduction of fluctuations. This approach is then pursued at the level of a spatial discretization of the gradient flow structure, specifically, by discretizing the energy functional and the dissipative metric tensor. This leads us to derive a stochastic differential equation that can be interpreted as an approximation of the stochastic thin film equation. Subsequently, we show that a suitable choice of the discrete mobility function results in solutions that strictly preserve positivity. The talk closes by discussing the probability of solutions to the stochastic thin film equation to approach zero.
14:30-15:00
Jonathan Weare (New York University)
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters. The method requires samples from the posterior distribution of the parameters for different values of the hyperparameters on a simulation grid and returns inference on the marginal likelihood defined everywhere on its domain, and on its functionals. We explain the relationship between the method and many of the methods that have been used in this context, including sequential Monte Carlo, Gibbs sampling, Monte Carlo maximum likelihood, and umbrella sampling. We establish the consistency of the proposed estimators as the sampling effort increases, both when the simulation grid is kept fixed and when it becomes dense in the domain. We showcase the approach on Gaussian process regression and classification and crossed effect models. The talk is based on joint work with Omiros Papaspiliopoulos and Timothee Stumpf-Fetizon.
15:00-15:30
Andre Wibisono (Yale University)
Sampling is a fundamental algorithmic task. Many sampling algorithms are based on discretization of the Langevin dynamics, which is the Wasserstein gradient flow for minimizing relative entropy on the space of probability distributions. In this talk, we discuss the Proximal Sampler algorithm, which is an approximate proximal discretization of the Langevin dynamics. We survey the mixing times of the Proximal Sampler and show that it achieves matching convergence guarantees with the Langevin dynamics in continuous time, and with the proximal point method from optimization. We illustrate the proof technique via establishing strong data processing inequalities for the Gaussian channel and its time reversal under isoperimetry.
15:30-16:00
José Blanchet (Stanford University)
Consider a population of N agents in which each agent can sequentially choose its individual action so as to maximize the total expected population reward over t time periods. An agent’s state evolves in accordance with the agent’s current state, its action, and the current empirical state-action distribution of the population. Such formulations arise naturally in many settings. We study the mean-field limit in which the number of agents N goes to infinity. Applying the Law of Large Numbers leads to a simpler deterministic mean-field optimization problem for which the optimality gap relative to solving the full N agent Markov decision process problem is typically of order N^{1/2}. In this talk, we discuss a control formulation in which the full N agent MDP is replaced instead by a stochastic control problem involving the Gaussian fluctuations around the mean field. Under appropriate Lipschitz assumptions on the problem data, we show that this problem exhibits an optimality gap of order O(1), and we argue that solving this Gaussian control problem is typically significantly easier than solving the full MDP. This is joint work with Sirui Lin and Peter Glynn.
16:00-16:30 Coffee Break
16:30-17:00
Kristin Kirchner (TU Delft & KTH Royal Institute of Technology)
Stochastic Volterra processes play an important role in finance, especially for modelling the variance process in rough stochastic volatility models. However, classical approaches to simulate these processes entail high computational costs, mainly caused by their lack to satisfy a Markov property. In recent years, the idea of approximating a non-Markovian stochastic Volterra process by a solution to a N-dimensional system of ordinary stochastic differential equations has gained popularity.
More specifically, the fractional kernel, arising e.g. for the variance process in the rough Bergomi and rough Heston models, allows for an integral representation using the Laplace transform which approximated by a quadrature with N nodes transforms stochastic Volterra equations with this kernel into systems of ordinary stochastic differential equations in R^N.
In this talk, I will discuss a new choice for the quadrature nodes and weights that renders the corresponding Markovian approximation to converge pathwise in Hölder norms, up to the maximal Hölder exponent prescribed by the regularity of exact solution, at a rate that is exponential in the square root of the number N of quadrature nodes. Numerical experiments for the rough Bergomi model verify our theoretical results.
This talk is based on joint work with Noé Corneille (TU Delft).
17:00-17:30
Benjamin Jourdain (École des Ponts ParisTech)
In this joint work with Stephane Menozzi, we are interested in the discretization of an SDE driven by a symmetric isotropic noise with stability index greater than one and with a drift belonging to a Lebesgue space with time and space indices satisfying a related Krylov-Rockner condition. We consider an Euler scheme with cutoffed drift where the time-variable is randomized. We estimate the norm of the difference between the densities of the diffusion and the Euler scheme in the dual of the spatial Lebesgue space for the drift. This natural choice permits to deal with the main error contribution by a Gronwall’s type argument. We investigate the preservation of the argument to other Lebesgue norms in order to also deal with the case, important in view of applications, when the drift is the sum of contributions in distinct Lebesgue spaces.
17:30-18:30 semi-plenary talk
Andreas Eberle (University of Bonn)
Non-reversible Markov Chain Monte Carlo methods promise to accelerate convergence to stationarity by overcoming diffusive behaviour. However, standard mathematical approaches that have been developed for deriving quantitative bounds for convergence to equilibrium of reversible Markov processes usually do not apply or do not yield sharp bounds in the non-reversible case. In this talk, we discuss different recently developed techniques to derive both lower and upper bounds on relaxation times of non-reversible Markov processes.
Many non-reversible Markov processes related to MCMC methods (and not only those) can be viewed as lifts of an underlying reversible process. One can then ask for the existence of optimal lifts corresponding to maximal convergence acceleration. In this context, properties of the generator of the reversible process can be leveraged to derive bounds for a non-reversible lift. We will discuss several examples including lifted random walks, kinetic Langevin dynamics, Hamiltonian Monte Carlo, Event Chain Monte Carlo, and a related local time process of a self-repellent random walk. In some cases, lifts of optimal convergence order can be identified, whereas in other cases, the derivation of matching upper and lower bounds is still an open problem.
Wednesday, 15 July
14:00-14:30
Andreas Neuenkirch (University of Mannheim)
Consensus-based optimization (CBO), introduced in [1,2], is a gradient-free consensus dynamics for approximating the global minimizer $x^{\star}$ of a possibly non-convex and non-smooth function $f: \mathbb{R}^D \rightarrow \mathbb{R}$. It combines consensus dynamics with stochastic exploration, and its convergence properties have been a very active field of research recently, see, e.g., [3,4,5,6].
In this talk, we study a zero-noise variant of CBO, which corresponds to a fully deterministic particle system $x_t=\big(x_t^1, \ldots, x_t^N\big) \in \mathbb{R}^{D \cdot N}$, $t \geq 0$, with $N$ particles, contraction rate $\lambda > 0$, and concentration parameter $\alpha > 0$. The initial particle configuration $x_0$ is constructed using low-discrepancy Quasi–Monte Carlo point sets, which provide a uniform coverage of the domain.
Under mild regularity assumptions on $f$, we show that the particle average $\overline{x}_t^N$ is close to the global minimizer. More precisely, we derive explicit bounds for $|\overline{x}_t^N – x^{\star}|$ in terms of the parameters of the system, using tools from Quasi–Monte Carlo as well as the Laplace principle. In particular, for a given target accuracy $\varepsilon > 0$, we quantify how to choose $N$, $\alpha$, $\lambda$, and the time $T$ such that $|\overline{x}_T^N – x^{\star}| \leq \varepsilon$.
This talk is based on joint work with Jacob Heieck and Simone G\”ottlich (Universität Mannheim). \begin{itemize}
\item[{[1]}] R. Pinnau, C. Totzeck, O. Tse, and S. Martin, A consensus-based model for global optimization
and its mean-field limit, Mathematical Models and Methods in Applied Sciences, 27 (2017), pp. 183–
204
\item[{[2]}] J.A. Carrillo, Y.-P. Choi, C. Totzeck, and O. Tse, An analytical framework for consensus-
based global optimization method, Mathematical Models and Methods in Applied Sciences, 28 (2018),pp. 1037–1066
\item[{[3]}] M. Fornasier, T. Klock, and K. Riedl,Consensus-based optimization methods converge globally, SIAM Journal on Optimization, 34
(2024), pp. 2973–3004
\item[{[4]}] N. Gerber, F. Hoffmann, D. Kim, and U. Vaes, Uniform-in-time propagation of chaos for
consensus-based optimization, 2025+
\item[{[5]}] S. Bonandin, K. Riedl, and S. Veneruso, Strong global convergence of the consensus-based
optimization algorithm, 2025+
\item[{[6]}] P. Bianchi, R.-A. Dragomir, and V. Priser, Consensus-Based Optimization Beyond Finite-Time Analysis, 2025+
\end{itemize}
14:30-15:00
Chengcheng Ling (University of Augsburg)
We study the weak convergence of a generic tamed Euler-Maruyama scheme for the kinetic stochastic differential equations (SDEs) with integrable drifts. We show that the marginal density of the considered scheme converges at rate 1/2 to the corresponding marginal density of the SDE. The convergence rate is independent from the criticality gap, which is new compared to previous results.
15:00-15:30
Eugen Bronasco (Chalmers University of Technology & University of Gothenburg)
15:30-16:00
Michaela Hitz (University of Klagenfurt)
A fundamental question in stochastic modelling is that of quantifying the effects of model uncertainty. In this context it is of interest to compute a distance between different stochastic models. A reasonable choice of distance is a modification of the Wasserstein distance on the space of probability measures called adapted Wasserstein distance, as it appears in bicausal optimal transport.
We solve constrained optimal transport problems in which the marginal laws are given by the laws of solutions of stochastic differential equations (SDEs). We consider SDEs with irregular coefficients, making only minimal regularity assumptions. Numerical methods are employed as a theoretical tool to bound the adapted Wasserstein distance. This opens the door for computing the adapted Wasserstein distance in a simple way. We show that this method can be applied to quantifying model uncertainty in stochastic optimisation problems.
Our approach successfully brings together optimal transport and numerical analysis of SDEs.
This talk is based on joint work with Benjamin A.Robinson (University of Klagenfurt).
16:00-16:30 Coffee Break
16:30-17:00
Sifan Liu (Duke University)
Sampling from complex distributions with isolated regions of probability mass remains a central challenge for classical Markov chain Monte Carlo methods. We introduce a Metropolis-adjusted sampler that constructs proposals along a diffusion path connecting the target distribution to a unimodal Gaussian reference. By evolving along this smooth interpolation, the sampler generates global proposals that can move efficiently between isolated modes. We analyze how the acceptance probability depends on the discretization step size, diffusion time horizon, and approximation errors in the learned diffusion, and derive optimal tuning guidelines in a high-dimensional scaling limit. We also discuss practical strategies for learning the diffusion path using variational methods, with an emphasis on mitigating mode collapse and reducing the cost of gradient evaluations. We demonstrate the effectiveness of the proposed method on challenging multimodal examples from Bayesian inference, where traditional tempering strategies can be unreliable.
17:00-17:30
Stephane Menozzi (Université Évry Paris-Saclay)
We discuss the weak error for a stochastic differential equation with isotropic stable additive noise and {non Lipschitz} drift, when considering an appropriate discretization scheme. We will in particular focus on drifts belonging to Hölder spaces or Besov spaces with negative regularity index. The error on the densities as well as the one associated with some suitable test functions will be presented.
17:30-18:00
Pierre Monmarché (Université Gustave Eiffel)
Motivated by many recent algorithms which are either designed as mean-field interacting particle systems or can be retrospectively interpreted as such, the question of establishing quantitative long-time estimates for these processes have received much interest over recent years. However, when the mean-field limit admits several stationary solutions (or possibly periodic orbits), particles are only ergodic at a time-scale which is out of reach for simulations. The classical tools can then only provide non-informative results. We will present a point of view to get relevant bounds on extremely large time-scales in this situation, and review some recent results in this direction.
18:00-18:30
Máté Gerencsér (TU Wien)
When approximating solutions of SPDEs, a basic challenge is that the rate of convergence is limited due to the low time and space regularity of the solution. In the context of additive space-time white noise driven semilinear SPDEs, the accelerated exponential Euler scheme by Jentzen and Kloeden was designed to overcome the temporal order barrier 1/4 — we first discuss the recent proof of this conjecture (joint work with Ana Djurdjevac and Helena Kremp). Then we move on to addressing the spatial order barrier 1/2, for which a new scheme is introduced and a higher strong convergence order 3/2 is proved (joint work with Lukas Anzeletti and Helena Kremp).
Posters
![[PZ13 – 2nd Floor]](https://focm2026.univie.ac.at/wp-content/uploads/2026/06/poster_zones_2-stock.png){kind=link}
Raphaël Barboni
(Bocconi University)
Non-reversible samplers based on Hamiltonian or kinetic Langevin dynamics have been shown to exhibit faster convergence rates than reversible samplers for strongly log-concave target distributions in continuous spaces. We propose novel and simple non-reversible sampling schemes based on Hamiltonian dynamics for sampling in discrete spaces. In particular, our methods admit computationally efficient zero-order discretizations requiring only function evaluations, in the spirit of gradient-free algorithms. We analyze scaling limits of these algorithms in the case of simple target distributions and compare their performances with that of standard non-reversible samplers, highlighting regimes where inertial mechanisms provide accelerated exploration of state-space.
Gijs Custers
(Chalmers University of Technology & University of Gothenburg)
We introduce a domain-preserving Lie-Trotter splitting scheme for approximating the solutions of some nonlinear SPDEs driven by a purely time-dependent Brownian motion. We prove strong convergence in time of this scheme with rate 1/2. Both the domain-preserving property and convergence of the proposed scheme are confirmed numerically and compared to standard numerical methods that do not preserve the domain. This is a joint work with Charles-Edouard Bréhier and David Cohen.
Francisco Navarro
(Universidad de Alicante)
Random differential equations (RDEs) are key tools to model dynamical systems under uncertainty. This work focuses on numerically approximating the time-dependent probability density function (PDF) of RDE solutions at fixed time instants. The random variable transformation (RVT) technique can deliver exact or approximate PDFs when the solution admits explicit, series, or semi-analytic representations, but its applicability is limited by the need for an invertible dependence on the input random variables. Other classical strategies include Monte Carlo simulation with kernel-based PDF reconstruction, which is universal but slowly convergent, and generalized polynomial chaos, which can converge spectrally for smooth problems but suffers from the curse of dimensionality.
This work proposes a new methodology that couples standard numerical initial value problem solvers with RVT to approximate the solution PDF for RDEs without explicit closed forms. The method constructs an auxiliary initial value problem for the parametric derivative of the solution, enabling PDF computation without explicit numerical inversion of the solution map, which is a major computational bottleneck in existing RVT-based numerical approaches. An error analysis is provided, proving that the relative error in the approximated PDF scales with the global error of the underlying numerical solver.
Stefan Oberdörster
(University of Bonn)
Recent progress on the theory of variational hypocoercivity established that Randomized Hamiltonian Monte Carlo—at criticality—can achieve pronounced ballistic acceleration of its convergence and hence sampling performance over diffusive dynamics. Manual critical tuning being infeasible in practice has motivated self-tuning algorithms, most notably the No-U-turn Sampler (NUTS). Due to its empirical success, NUTS has become the default sampler in many probabilistic programming languages.
Beyond empirics however, a rigorous understanding of NUTS’ ability to achieve acceleration has been missing. We initiate this study, combining a concentration of measure approach to the self-tuning mechanism with a coupling-based mixing analysis for Hamiltonian Monte Carlo.
The developed theory provides fundamentally new insight into NUTS’ performance, with two aspects being particularly notable:
On the one hand, we give the first rigorous explanation of NUTS’ ability to achieve acceleration in a class of challenging, realistic target distributions—ill-conditioned, high-dimensional geometric Toeplitz Gaussians.
On the other hand, we discover previously unknown limitations to this ability by conducting a detailed study of NUTS in high-dimensional two-scale Gaussians, products of two high-dimensional isotropic Gaussians.
Specifically, we show that while NUTS is accelerated in some of these targets, in others NUTS fails to achieve acceleration, reverting to diffusive mixing.
Asymptotically, we establish a phase transition in the space of two-scale Gaussians separating ballistic and diffusive mixing of NUTS.
The discovered limitations emphasize the importance of pursuing a deeper understanding of the self-tuning mechanism of NUTS in order to ensure acceleration is achieved in practical applications.
Almut Rödder
(ETH Zurich)
Many statistical estimation problems, including synchronization, community detection, and mixture models, exhibit inherent global symmetries: the latent signal is identifiable only up to a group action, such as a global sign flip, permutation, or relabeling. For example, in the two-community stochastic block model, if $x\in{\pm1}^n$ represents community memberships, then x and -x encode the same partition. For Bayesian statistics, these symmetries can create several equivalent posterior modes, separated by bottlenecks. A local MCMC algorithm such as Glauber dynamics may therefore mix very slowly, even though the different modes represent the same statistical answer.
We aim to distinguish this artificial slow mixing from the actual difficulty of sampling the posterior modulo its symmetry. The idea is to add a symmetry-correction step to the Glauber dynamics, such as a global spin flip, and introduce the notion of quotient mixing. We describe a stochastic localization-based framework for proving mixing time bounds for this quotient dynamics. The main contribution is a variance-decay decomposition for functions that are invariant under the symmetry: instead of trying to control the covariance of the full symmetric measure, we decompose the localized measures into symmetry-broken pieces and control those pieces separately.
As a test case, we apply the method to the low-temperature Curie-Weiss model. Classical Glauber dynamics mixes slowly because it has to cross the bottleneck between the two magnetized phases. On the other hand, the quotient dynamics, where the two phases are identified by a spin flip, mixes in polynomial time. We recover a polynomial mixing bound for the quotient dynamics through our framework, providing a new proof that illustrates the scope of the method.
This is joint work with Afonso Bandeira and Yuansi Chen.
Roy Schieven
(University of Amsterdam)
Markov chain Monte Carlo (MCMC) methods based on kinetic Langevin diffusions are widely used in sampling problems. Non-asymptotic total variation mixing time bounds can be obtained from existing bounds in Wasserstein distance via a Wasserstein-to-TV regularization argument. In recent years, coupling-based frameworks have been developed in related settings to perform this regularization, typically using Markovian couplings. In this poster, we argue that Markovian couplings for discretizations of the kinetic Langevin equation lead to total variation bounds that are essentially uninformative. We introduce a novel, explicit non-Markovian coupling based on the work of Chak & Monmarché (2025). For the OBABO splitting scheme, the structure of the update makes the quantitative analysis of this coupling particularly straightforward, allowing us to recover known non-asymptotic total variation bounds under standard assumptions that allow for nonconvex potentials. The coupling is fully implementable, and we illustrate its behavior numerically.
This is joint work with Nawaf Bou-Rabee and Sonja Cox.
Alexander Söllinger
(University of Klagenfurt)
We aim to compare the laws of solutions to stochastic differential equations (SDEs) with jumps. A natural choice of metric on the space of probability measures is the Wasserstein distance. However, the Wasserstein distance does not account for the structure of the flow of information of the underlying stochastic process. Therefore, a new metric—the bicausal Wasserstein distance—was introduced.
We investigate how to compute this distance for a class of SDEs with jumps. To this end, we employ tools from adapted optimal transport in order to identify an explicit optimizer. We then modify the Euler–Maruyama scheme so that it is monotone at each time step. This ensures optimality for the discretized transport problem and yields a sequence of solutions converging to the value of the continuous problem.
In a second step, we generalize this result by employing a transformation-based approach built on the Euler–Maruyama scheme and also analyzing their behavior for different driving jump processes.
Ruizhe Zhang
(Wuhan University)
We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability–flow ordinary differential equation (ODE) derived from linear stochastic interpolants. The key innovation of our approach is the use of a sequence of Langevin samplers to enable efficient simulation of the flow. Specifically, these Langevin samplers are employed (i) to generate samples from the interpolant distribution at intermediate times and (ii) to construct, starting from these intermediate times, a robust estimator of the velocity field governing the flow ODE. For both applications of the Langevin diffusions, we establish convergence guarantees in the $W_2$ distance. Extensive numerical experiments demonstrate the efficiency of the proposed method on challenging multimodal distributions across a range of dimensions, as well as its effectiveness in Bayesian inference tasks.