Related papers: Learning the temporal evolution of multivariate de…
A phenomenological model for the dissipation of scalar fluctuations due to the straining by the fluid motion is proposed in this letter. An explicit equation is obtained for the time evolution of the probability distribution function of a…
The Fokker-Planck equation can be reformulated as a continuity equation, which naturally suggests using the associated velocity field in particle flow methods. While the resulting probability flow ODE offers appealing properties - such as…
Data often are formed of multiple modalities, which jointly describe the observed phenomena. Modeling the joint distribution of multimodal data requires larger expressive power to capture high-level concepts and provide better data…
We propose a deep learning approach to probabilistic forecasting of macroeconomic and financial time series. Being able to learn complex patterns from a data rich environment, our approach is useful for a decision making that depends on…
This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of…
The study of the density evolution naturally arises in Mean Field Game theory for the estimation of the density of the large population dynamics. In this paper, we study the density evolution of McKean-Vlasov stochastic differential…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
Given a discrete stochastic process, for example a chemical reaction system or a birth and death process, we often want to find a continuous stochastic approximation so that the techniques of stochastic differential equations may be brought…
We introduce manifold-learning flows (M-flows), a new class of generative models that simultaneously learn the data manifold as well as a tractable probability density on that manifold. Combining aspects of normalizing flows, GANs,…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
In this work, we consider the solvability of the Fokker-Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker-Planck equation…
The Fokker-Planck equation describes the evolution of the probability density associated with a stochastic differential equation. As the dimension of the system grows, solving this partial differential equation (PDE) using conventional…
Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data…
Generalising well in supervised learning tasks relies on correctly extrapolating the training data to a large region of the input space. One way to achieve this is to constrain the predictions to be invariant to transformations on the input…
A flow matching model learns a time-dependent vector field $v_t(x)$ that generates a probability path $\{ p_t \}_{0 \leq t \leq 1}$ that interpolates between a well-known noise distribution ($p_0$) and the data distribution ($p_1$). It can…
In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…
Learning the multivariate distribution of data is a core challenge in statistics and machine learning. Traditional methods aim for the probability density function (PDF) and are limited by the curse of dimensionality. Modern neural methods…
Normalizing flows model complex probability distributions by combining a base distribution with a series of bijective neural networks. State-of-the-art architectures rely on coupling and autoregressive transformations to lift up invertible…
In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality observing the…
A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium…