Related papers: Particle Flow Bayes' Rule
Optical flow estimation with convolutional neural networks (CNNs) has recently solved various tasks of computer vision successfully. In this paper we adapt a state-of-the-art approach for optical flow estimation to omnidirectional images.…
The goal of this paper is to determine the laws of observed trajectories assuming that there is a mechanical system in the background and using these laws to continue the observed motion in a plausible way. The laws are represented by…
Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex…
Mechanistic models with differential equations are a key component of scientific applications of machine learning. Inference in such models is usually computationally demanding, because it involves repeatedly solving the differential…
We harness the physics-informed neural network (PINN) approach to extend the utility of phenomenological models for particle migration in shear flow. Specifically, we propose to constrain the neural network training via a model for the…
Pretraining for partial differential equation (PDE) modeling has recently shown promise in scaling neural operators across datasets to improve generalizability and performance. Despite these advances, our understanding of how pretraining…
We prove H\"{o}lder regularity for the trajectories of an interacting particle system. The particle velocities are given by the nonlocal and singular interactions with the other particles. Particle collisions occur in finite time. Prior to…
The brief works of Peierls on the role of the observer in quantum mechanics are examined, interpreted and expanded to widen accessibility and understanding of these works. The approach followed here is very much in the spirit adopted by…
The goal of this thesis is to develop the optimisation and generalisation theoretic foundations of learning in artificial neural networks. On optimisation, a new theoretical framework is proposed for deriving architecture-dependent…
We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…
We introduce a model detector which registers the passage of a particle through the detector location, without substantially perturbing the particle wave function. (The exact time of passage is not determined in such measurements.) We then…
Boundary conditions (BCs) are important groups of physics-enforced constraints that are necessary for solutions of Partial Differential Equations (PDEs) to satisfy at specific spatial locations. These constraints carry important physical…
Extended object tracking methods based on random matrices, founded on Bayesian filters, have been able to achieve efficient recursive processes while jointly estimating the kinematic states and extension of the targets. Existing random…
Bayesian observer and actor models have provided normative explanations for many behavioral phenomena in perception, sensorimotor control, and other areas of cognitive science and neuroscience. They attribute behavioral variability and…
We show that many machine-learning algorithms are specific instances of a single algorithm called the \emph{Bayesian learning rule}. The rule, derived from Bayesian principles, yields a wide-range of algorithms from fields such as…
Object Detection (OD) is an important task in Computer Vision with many practical applications. For some use cases, OD must be done on videos, where the object of interest has a periodic motion. In this paper, we formalize the problem of…
In this paper, we propose a convolutional layer inspired by optical flow algorithms to learn motion representations. Our representation flow layer is a fully-differentiable layer designed to capture the `flow' of any representation channel…
Motion detection is a fundamental but challenging task for autonomous driving. In particular scenes like highway, remote objects have to be paid extra attention for better controlling decision. Aiming at distant vehicles, we train a neural…
Interacting particle systems play a key role in science and engineering. Access to the governing particle interaction law is fundamental for a complete understanding of such systems. However, the inherent system complexity keeps the…
We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…