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Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…

Active learning optimizes the exploration of large parameter spaces by strategically selecting which experiments or simulations to conduct, thus reducing resource consumption and potentially accelerating scientific discovery. A key…

The ability to learn polynomials and generalize out-of-distribution is essential for simulation metamodels in many disciplines of engineering, where the time step updates are described by polynomials. While feed forward neural networks can…

A novel scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. The idea is to consider a certain open-system evolution,…

This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…

Bayesian flow networks (BFNs) iteratively refine the parameters, instead of the samples in diffusion models (DMs), of distributions at various noise levels through Bayesian inference. Owing to its differentiable nature, BFNs are promising…

Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…

Bayesian Optimization (BO) is an efficient tool for optimizing black-box functions, but its theoretical guarantees typically hold in the asymptotic regime. In many critical real-world applications such as drug discovery or materials design,…

Clinical investigators are increasingly interested in discovering computational biomarkers from short-term longitudinal omics data sets. This work focuses on Bayesian regression and variable selection for longitudinal omics datasets, which…

Multiscale dynamical systems characterized by interacting fast and slow processes are ubiquitous across scientific domains, from climate dynamics to fluid mechanics. Accurate modeling of such systems requires capturing both the long-term…

Self-similarity is widely considered the reference framework for modeling the scaling properties of real-world data. However, most theoretical studies and their practical use have remained univariate. Operator Fractional Brownian Motion…

In many signal processing applications it is required to estimate the unobservable state of a dynamic system from its noisy measurements. For linear dynamic systems with Gaussian Mixture (GM) noise distributions, Gaussian Sum Filters (GSF)…

Probabilistic generative models based on measure transport, such as diffusion and flow-based models, are often formulated in the language of Markovian stochastic dynamics, where the choice of the underlying process impacts both algorithmic…

Despite its empirical success and recent theoretical progress, there generally lacks a quantitative analysis of the effect of batch normalization (BN) on the convergence and stability of gradient descent. In this paper, we provide such an…

Coarse-graining (CG) of molecular simulations simplifies the particle representation by grouping selected atoms into pseudo-beads and drastically accelerates simulation. However, such CG procedure induces information losses, which makes…

As evolutionary algorithms (EAs) are general-purpose optimization algorithms, recent theoretical studies have tried to analyze their performance for solving general problem classes, with the goal of providing a general theoretical…

Parameter calibration is essential for reducing uncertainty and improving predictive fidelity in physics-based models, yet it is often limited by the high computational cost of model evaluations. Bayesian calibration methods provide a…

Stateful optimizers maintain gradient statistics over time, e.g., the exponentially smoothed sum (SGD with momentum) or squared sum (Adam) of past gradient values. This state can be used to accelerate optimization compared to plain…

Generalized Bayesian Inference (GBI) tempers a loss with a temperature $\beta > 0$ to mitigate overconfidence and improve robustness under model misspecification, but existing GBI methods typically rely on costly MCMC or SDE-based samplers…