Related papers: Fokker-Planck Score Learning: Efficient Free-Energ…
One of the obstacles hindering the scaling-up of the initial successes of machine learning in practical engineering applications is the dependence of the accuracy on the size of the database that "drives" the algorithms. Incorporating the…
We develop the neural network based "learning from regression uncertainty" approach for automated detection of phases of matter in nonequilibrium active systems. Taking the flocking phase transition of self-propelled active particles…
We introduce a practical method for incorporating equality and inequality constraints in global optimization methods based on stochastic interacting particle systems, specifically consensus-based optimization (CBO) and ensemble Kalman…
Predictive Coding (PC) is an influential account of cortical learning. Much of recent work has focused on comparing PC to Backpropagation (BP) to find whether PC offers any advantages. Small scale experiments show that PC enables learning…
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
We present a method to explore the free energy landscapes of chemical reactions with post-transition-state bifurcations using an enhanced sampling method based on well-tempered metadynamics. Obviating the need for computationally expensive…
We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one…
This study aims to improve the spatial representation of uncertainties when regressing surface wind speeds from large-scale atmospheric predictors for sub-seasonal forecasting. Sub-seasonal forecasting often relies on large-scale…
In this paper we analyze the global existence of classical solutions to the initial boundary-value problem for a nonlinear parabolic equation describing the collective behavior of an ensemble of neurons. These equations were obtained as a…
Diffusion models achieve remarkable generation quality, yet face a fundamental challenge known as memorization, where generated samples can replicate training samples exactly. We develop a theoretical framework to explain this phenomenon by…
We derive, from first principle, the Fokker-Planck equation describing the non-perturbative real-time evolution of a gauge field at high temperatures on the spatial scale $(g^2T)^{-1}$ and the time scale $(g^4T)^{-1}$, where $g$ is the…
Recent work has shown that diffusion models trained with the denoising score matching (DSM) objective often violate the Fokker--Planck (FP) equation that governs the evolution of the true data density. Directly penalizing these deviations…
Diffusion models produce impressive results in modalities ranging from images and video to protein design and text. However, generating samples with user-specified properties remains a challenge. Recent research proposes fine-tuning models…
We report in this paper a fast and accurate algorithm for computing the exact spherical nonreflecting boundary condition (NRBC) for time-dependent Maxwell's equations. It is essentially based on a new formulation of the NRBC, which allows…
A novel experimental paradigm and a novel modelling approach are presented to investigate oscillatory human motor performance by means of a key concept from condensed matter physics, namely, thermodynamic state variables. To this end, in…
Simulating Markovian open quantum systems in the semiclassical regime poses a grand challenge for computational physics, as the highly oscillatory nature of the dynamics imposes prohibitive resolution requirements on traditional grid-based…
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate…
We demonstrate how a prior assumption of smoothness can be used to enhance the reconstruction of free energy profiles from multiple umbrella sampling simulations using the Bayesian Gaussian process regression approach. The method we derive…
A common goal in observational research is to estimate marginal causal effects in the presence of confounding variables. One solution to this problem is to use the covariate distribution to weight the outcomes such that the data appear…
A theoretical framework is developed for the phenomenon of non-Gaussian normal diffusion that has experimentally been observed in several heterogeneous systems. From the Fokker-Planck equation with the dynamical structure with largely…