Related papers: Differentiable programming for particle physics si…
An open source software package for simulating thermal neutron propagation in geometry is presented. In this system, neutron propagation can be treated by either the particle transport method or the ray-tracing method. Supported by an…
Nano- to micro-sized particles with differently charged surface areas exhibit complex interaction patterns, characterized by both opposite-charge attraction and like-charge repulsion. While several successful models have been proposed in…
Combustion kinetic modeling is an integral part of combustion simulation, and extensive studies have been devoted to developing both high fidelity and computationally affordable models. Despite these efforts, modeling combustion kinetics is…
We discuss the great importance of using mathematical software in solving problems in today's society. In particular, we show how to use Mathematica software to solve ordinary differential equations exactly and numerically. We also show how…
We extend the scope of differential machine learning and introduce a new breed of supervised principal component analysis to reduce dimensionality of Derivatives problems. Applications include the specification and calibration of pricing…
We present two analytical formulae for estimating the sensitivity -- namely, the gradient or Jacobian -- at given realizations of an arbitrary-dimensional random vector with respect to its distributional parameters. The first formula…
Bayesian parameter inference for complex stochastic simulators is challenging due to intractable likelihood functions. Existing simulation-based inference methods often require large number of simulations and become costly to use in…
We introduce a `virtual-move' Monte Carlo (VMMC) algorithm for systems of pairwise-interacting particles. This algorithm facilitates the simulation of particles possessing attractions of short range and arbitrary strength and geometry, an…
For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced by approximations to a distribution's inverse cumulative distribution function. These approximations are…
This article analyzes and develops a method to solve fractional ordinary differential equations using the Monte Carlo Method. A numerical simulation is performed for some differential equations, comparing the results with what exists in the…
The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients…
Originally designed for applications in computer graphics, visual computing (VC) methods synthesize information about physical and virtual worlds, using prescribed algorithms optimized for spatial computing. VC is used to analyze geometry,…
Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the…
The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability…
We consider the problem of efficiently computing the derivative of the solution map of a convex cone program, when it exists. We do this by implicitly differentiating the residual map for its homogeneous self-dual embedding, and solving the…
Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the…
We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient…
Objective. Algorithmic differentiation (AD) can be a useful technique to numerically optimize design and algorithmic parameters by, and quantify uncertainties in, computer simulations. However, the effectiveness of AD depends on how…
We propose a sequential Monte Carlo algorithm for parameter learning when the studied model exhibits random discontinuous jumps in behaviour. To facilitate the learning of high dimensional parameter sets, such as those associated to neural…
Sequential Monte Carlo (SMC), or particle filtering, is widely used in nonlinear state-space systems, but its performance often suffers from poorly approximated proposal and state-transition distributions. This work introduces a…