Related papers: Particle Flow Bayes' Rule

In this paper, we propose a progressive Bayesian procedure, where the measurement information is continuously included into the given prior estimate (although we perform observations at discrete time steps). The key idea is to derive a…

Neural ordinary differential equations (Neural ODEs) propose the idea that a sequence of layers in a neural network is just a discretisation of an ODE, and thus can instead be directly modelled by a parameterised ODE. This idea has had…

Neural networks have recently been used to analyze diverse physical systems and to identify the underlying dynamics. While existing methods achieve impressive results, they are limited by their strong demand for training data and their weak…

Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of…

The particle filter is a popular Bayesian filtering algorithm for use in cases where the state-space model is nonlinear and/or the random terms (initial state or noises) are non-Gaussian distributed. We study the behavior of the error in…

Continuous normalizing flows (CNFs) construct invertible mappings between an arbitrary complex distribution and an isotropic Gaussian distribution using Neural Ordinary Differential Equations (neural ODEs). It has not been tractable on…

Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate models for the…

A general approach for Bayesian filtering of multi-object systems is studied, with particular emphasis on the model where each object generates observations independently of other objects. The approach is based on variational calculus…

Optical flow provides information on relative motion that is an important component in many computer vision pipelines. Neural networks provide high accuracy optical flow, yet their complexity is often prohibitive for application at the edge…

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…

We propose and demonstrate a novel scheme for optical nanoparticle characterization, optofluidic force induction (OF2i), which achieves real-time optical counting with single-particle sensitivity, high throughput, and for particle sizes…

Particle filtering is a popular method for inferring latent states in stochastic dynamical systems, whose theoretical properties have been well studied in machine learning and statistics communities. In many control problems, e.g.,…

Optical flow refers to the visual motion observed between two consecutive images. Since the degree of freedom is typically much larger than the constraints imposed by the image observations, the straightforward formulation of optical flow…

We propose a recursive particle filter for high-dimensional problems that inherently never degenerates. The state estimate is represented by deterministic low-discrepancy particle sets. We focus on the measurement update step, where a…

Bayes' rule, which is routinely used to update beliefs based on new evidence, can be derived from a principle of minimum change. This principle states that updated beliefs must be consistent with new data, while deviating minimally from the…

Modern Bayesian inference involves a mixture of computational techniques for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows for data analysis. Typical problems in Bayesian workflows…

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…

Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately current approaches fall short when the underlying space has a non trivial topology, and are only…

Neural operator surrogates for time-dependent partial differential equations (PDEs) conventionally employ autoregressive prediction schemes, which accumulate error over long rollouts and require uniform temporal discretization. We introduce…

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…