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Diffusion models as probabilistic neural operators for recovering unobserved states of dynamical systems
In this work, we show that diffusion-based generative models exhibit many properties favourable for neural operators, and they can effectively generate the solution of a PDE conditionally on the parameter or recover the unobserved parts of the system.
In-Context Symbolic Regression: Leveraging Language Models for Function Discovery
Symbolic Regression (SR) is a task which aims to extract the mathematical expression underlying a set of empirical observations.
Improved Training of Physics-Informed Neural Networks with Model Ensembles
Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data.
Learning Trajectories of Hamiltonian Systems with Neural Networks
A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's equations of motion.
A Grid-Structured Model of Tubular Reactors
We propose a grid-like computational model of tubular reactors.
