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We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
Stochastic resetting, a diffusive process whose amplitude is "reset" to the origin at random times, is a vividly studied strategy to optimize encounter dynamics, e.g., in chemical reactions. We here generalize the resetting step by…
We study a new aggregation operator for gradients coming from a mini-batch for stochastic gradient (SG) methods that allows a significant speed-up in the case of sparse optimization problems. We call this method AdaBatch and it only…
Text-to-image diffusion models exhibit strong generative performance but remain highly sensitive to prompt formulation, often requiring extensive manual trial and error to obtain satisfactory results. This motivates the development of…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
We study the problem of how to distribute the training of large-scale deep learning models in the parallel computing environment. We propose a new distributed stochastic optimization method called Elastic Averaging SGD (EASGD). We analyze…
In this paper, we present a sequential sampling-based algorithm for the two-stage distributionally robust linear programming (2-DRLP) models. The 2-DRLP models are defined over a general class of ambiguity sets with discrete or continuous…
We present an approach to the dynamics of interacting particle systems, which allows to derive path integral formulas from purely stochastic considerations. We show that the resulting field theory is a dual version of the standard theory of…
We present a theoretical analysis of some popular adaptive Stochastic Gradient Descent (SGD) methods in the small learning rate regime. Using the stochastic modified equations framework introduced by Li et al., we derive effective…
Diffusion policies have recently emerged as a powerful class of visuomotor controllers for robot manipulation, offering stable training and expressive multi-modal action modeling. However, existing approaches typically treat action…
This paper proposes an algorithm to efficiently solve multistage stochastic programs with block separable recourse where each recourse problem is a multistage stochastic program with stage-wise independent uncertainty. The algorithm first…
We present a new approach to the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field,…
Modeling sequential data has become more and more important in practice. Some applications are autonomous driving, virtual sensors and weather forecasting. To model such systems so called recurrent models are used. In this article we…
In this paper, we study distributionally risk-receptive and distributionally robust (or risk-averse) multistage stochastic mixed-integer programs (denoted by DRR- and DRO-MSIPs). We present cutting plane-based and reformulation-based…
We consider a sequence of systems of Hawkes processes having mean field interactions in a diffusive regime. The stochastic intensity of each process is a solution of a stochastic differential equation driven by N independent Poisson random…
We propose a new discontinuous Galerkin Isogeometric Analysis (IgA) technique for the numerical solution of elliptic diffusion problems in computational domains decomposed into volumetric patches with non-matching interfaces. Due to an…
We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…
We propose a collision-oriented particle system to approximate a class of Landau-type equations. This particle system is formally derived from a particle system with random collisions in the grazing regime, and happens to be a special…
Stochastic particle-optimization sampling (SPOS) is a recently-developed scalable Bayesian sampling framework that unifies stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) algorithms based on Wasserstein…
Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…