Related papers: Feynman-Kac Operator Expectation Estimator
The expectation-maximization (EM) algorithm is an iterative computational method to calculate the maximum likelihood estimators (MLEs) from the sample data. It converts a complicated one-time calculation for the MLE of the incomplete data…
Conditional Flow Matching(CFM) represents a fast and high-quality approach to generative modelling, but in many applications it is of interest to steer the generated samples towards precise requirements. While steering approaches like…
For dynamical systems involving decision making, the success of the system greatly depends on its ability to make good decisions with incomplete and uncertain information. By leveraging the Koopman operator and its adjoint property, we…
The large-scale integration of renewable energy sources introduces significant operational uncertainty into power systems. Although Polynomial Chaos Expansion (PCE) provides an efficient tool for uncertainty quantification (UQ) in power…
We develop an asynchronous event-driven First-Passage Kinetic Monte Carlo (FPKMC) algorithm for continuous time and space systems involving multiple diffusing and reacting species of spherical particles in two and three dimensions. The…
The Feynman-Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, being a…
A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE). In existing samplers, the coefficients of the ODE solvers are pre-determined by the ODE formulation, the reverse discrete…
Generative models, particularly Diffusion Models (DM), have shown strong potential for Computed Tomography (CT) reconstruction serving as expressive priors for solving ill-posed inverse problems. However, diffusion-based reconstruction…
In the Feynman-Kac[1] path integral approach the eigenvalues of a quantum system can be computed using Wiener measure which uses Brownian particle motion. In our previous work[2-3] on such systems we have observed that the Wiener process…
Accurately predicting protein-ligand binding free energies (BFEs) remains a central challenge in drug discovery, particularly because the most reliable methods, such as free energy perturbation (FEP), are computationally intensive and…
Optimal experimental design (OED) is a framework that leverages a mathematical model of the experiment to identify optimal conditions for conducting the experiment. Under a Bayesian approach, the design objective function is typically…
Distributed phased arrays are comprised of separate, smaller antenna systems that coordinate with each other to support coherent beamforming towards a destination. However, due to the frequency drift and phase jitter of the oscillators, as…
This paper introduces a generative AI approach to probabilistic forecasting of real-time electricity market signals, including locational marginal prices, interregional price spreads, and demand-supply imbalances. We present WIAE-GPF, a…
The geometry of dynamical systems estimated from trajectory data is a major challenge for machine learning applications. Koopman and transfer operators provide a linear representation of nonlinear dynamics through their spectral…
The Variational Quantum Eigensolver (VQE) is a quantum algorithm used to find the ground state energy of a given Hamiltonian. The key component of VQE is the ansatz, which is a trial wavefunction that the algorithm uses to approximate the…
Bayesian inference in the physical sciences faces a fundamental challenge: the imperative for high-fidelity physical modeling often clashes with the intrinsic limitations of stochastic sampling algorithms. Complex, high-dimensional…
Wireless sensor networks (WSNs) represent a critical research domain within the Internet of Things (IoT) technology. The distributed Kalman filter (DKF) has garnered significant attention as an information fusion method for WSNs. However,…
We propose a novel method for simulating conditioned diffusion processes (diffusion bridges) in Euclidean spaces. By training a neural network to approximate bridge dynamics, our approach eliminates the need for computationally intensive…
The displacement distribution of a water molecular is characterized mathematically as Gaussianity without considering potential diffusion barriers and compartments. However, this is not true in real scenario: most biological tissues are…
This paper presents a partial state of the art about the topic of representation of generalized Fokker-Planck Partial Differential Equations (PDEs) by solutions of McKean Feynman-Kac Equations (MFKEs) that generalize the notion of McKean…