Search Results for author: Maxwell X. Cai

Found 4 papers, 4 papers with code

$ρ$-Diffusion: A diffusion-based density estimation framework for computational physics

1 code implementation13 Dec 2023 Maxwell X. Cai, Kin Long Kelvin Lee

In physics, density $\rho(\cdot)$ is a fundamentally important scalar function to model, since it describes a scalar field or a probability density function that governs a physical process.

Denoising Density Estimation +1

A hybrid approach for solving the gravitational N-body problem with Artificial Neural Networks

1 code implementation31 Oct 2023 Veronica Saz Ulibarrena, Philipp Horn, Simon Portegies Zwart, Elena Sellentin, Barry Koren, Maxwell X. Cai

To increase the robustness of a method that uses neural networks, we propose a hybrid integrator that evaluates the prediction of the network and replaces it with the numerical solution if considered inaccurate.

Numerical Integration

Neural Symplectic Integrator with Hamiltonian Inductive Bias for the Gravitational $N$-body Problem

1 code implementation28 Nov 2021 Maxwell X. Cai, Simon Portegies Zwart, Damian Podareanu

The gravitational $N$-body problem, which is fundamentally important in astrophysics to predict the motion of $N$ celestial bodies under the mutual gravity of each other, is usually solved numerically because there is no known general analytical solution for $N>2$.

Inductive Bias

Fast and Credible Likelihood-Free Cosmology with Truncated Marginal Neural Ratio Estimation

4 code implementations15 Nov 2021 Alex Cole, Benjamin Kurt Miller, Samuel J. Witte, Maxwell X. Cai, Meiert W. Grootes, Francesco Nattino, Christoph Weniger

Sampling-based inference techniques are central to modern cosmological data analysis; these methods, however, scale poorly with dimensionality and typically require approximate or intractable likelihoods.

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