Related papers: Gibbs Phenomenon Suppression in PDE-Based Statisti…

A generalisation of Takens' delay-coordinate embedding theorem to stochastic systems, the Stochastic Embedding Sufficiency Theorem, is an inverse methodology enabling non-parametric recovery of both drift and diffusion fields from scalar…

We show how decimated Gibbs measures which have an unbroken continuous symmetry due to the Mermin-Wagner theorem, although their discrete equivalents have a phase transition, still can become non-Gibbsian. The mechanism rests on the…

The normal forms up to the third order for a Hopf-steady state bifurcation of a general system of partial functional differential equations (PFDEs) is derived based on the center manifold and normal form theory of PFDEs. This is a…

We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…

We develop a domain-decomposition model reduction method for linear steady-state convection-diffusion equations with random coefficients. Of particular interest to this effort are the diffusion equations with random diffusivities, and the…

We consider Bayesian inference from multiple time series described by a common state-space model (SSM) structure, but where different subsets of parameters are shared between different submodels. An important example is disease-dynamics,…

As a typical quantum many body problem, we consider the time evolution of density matrix elements in the Bose-Hubbard model. For an arbitrary initial state, these quantities can be obtained from an SDE or stochastic differential equation…

Diffusion models provide expressive priors for forecasting trajectories of dynamical systems, but are typically unreliable in the sparse data regime. Physics-informed machine learning (PIML) improves reliability in such settings; however,…

We propose experimentally feasible ways to probe universal features of absorbing phase transitions from two different approaches, both based on numerical validations. On one hand, we numerically study a probability distribution of…

A model in statistical mechanics, characterised by the corresponding Gibbs measure, is a subset of the totality of probability distributions on the phase space. The shape of this subset, i.e., the geometry, then plays an important role in…

Modelling partial differential equations (PDEs) is of crucial importance in science and engineering, and it includes tasks ranging from forecasting to inverse problems, such as data assimilation. However, most previous numerical and machine…

Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations…

We develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics $d\mathbf{X}_t = a(\mathbf{X}_t)dt + \mathbf{b}(\mathbf{X}_t)d\mathbf{W}_t$. We formulate descriptions…

Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles.…

As Diffusion Models have shown promising performance, a lot of efforts have been made to improve the controllability of Diffusion Models. However, how to train Diffusion Models to have the disentangled latent spaces and how to naturally…

Generative modeling has recently undergone remarkable advancements, primarily propelled by the transformative implications of Diffusion Probabilistic Models (DPMs). The impressive capability of these models, however, often entails…

Finite mixture models are frequently used to uncover latent structures in high-dimensional datasets (e.g.\ identifying clusters of patients in electronic health records). The inference of such structures can be performed in a Bayesian…

Many stellar systems exhibit a finite spatial extent, yet constructing self-consistent spherical models with a prescribed outer boundary is non-trivial because sharp density cutoffs introduce discontinuities that lead to inconsistencies in…

Spectral reconstructions provide rigorous means to remove the Gibbs phenomenon and accelerate the convergence of spectral solutions in non-smooth differential equations. In this paper, we show the concurrent emergence of truncated…

A new type of dependent thinning for point processes in continuous space is proposed, which leverages the advantages of determinantal point processes defined on finite spaces and, as such, is particularly amenable to statistical, numerical,…