2 research outputs found
Local Convolution Enhanced Global Fourier Neural Operator For Multiscale Dynamic Spaces Prediction
Neural operators extend the capabilities of traditional neural networks by
allowing them to handle mappings between function spaces for the purpose of
solving partial differential equations (PDEs). One of the most notable methods
is the Fourier Neural Operator (FNO), which is inspired by Green's function
method and approximate operator kernel directly in the frequency domain. In
this work, we focus on predicting multiscale dynamic spaces, which is
equivalent to solving multiscale PDEs. Multiscale PDEs are characterized by
rapid coefficient changes and solution space oscillations, which are crucial
for modeling atmospheric convection and ocean circulation. To solve this
problem, models should have the ability to capture rapid changes and process
them at various scales. However, the FNO only approximates kernels in the
low-frequency domain, which is insufficient when solving multiscale PDEs. To
address this challenge, we propose a novel hierarchical neural operator that
integrates improved Fourier layers with attention mechanisms, aiming to capture
all details and handle them at various scales. These mechanisms complement each
other in the frequency domain and encourage the model to solve multiscale
problems. We perform experiments on dynamic spaces governed by forward and
reverse problems of multiscale elliptic equations, Navier-Stokes equations and
some other physical scenarios, and reach superior performance in existing PDE
benchmarks, especially equations characterized by rapid coefficient variations.Comment: 10 pages, 4 figure
ODE-based Recurrent Model-free Reinforcement Learning for POMDPs
Neural ordinary differential equations (ODEs) are widely recognized as the
standard for modeling physical mechanisms, which help to perform approximate
inference in unknown physical or biological environments. In partially
observable (PO) environments, how to infer unseen information from raw
observations puzzled the agents. By using a recurrent policy with a compact
context, context-based reinforcement learning provides a flexible way to
extract unobservable information from historical transitions. To help the agent
extract more dynamics-related information, we present a novel ODE-based
recurrent model combines with model-free reinforcement learning (RL) framework
to solve partially observable Markov decision processes (POMDPs). We
experimentally demonstrate the efficacy of our methods across various PO
continuous control and meta-RL tasks. Furthermore, our experiments illustrate
that our method is robust against irregular observations, owing to the ability
of ODEs to model irregularly-sampled time series.Comment: Accepted by NeurIPS 202