A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
WSINDy algorithm proves robust to noise in identifying differential equations.
ESNs with transfer learning predict long-term chaotic patterns in spatiotemporal dynamical systems.
MEDIDA discovers model errors in chaotic systems using sparse regression and data assimilation.
This note introduces a regression technique for finding a class of nonlinear integro-differential operators from data. The method parametrizes the spatial operator with neural networks and Fourier transforms such that it can fit a class of nonlinear operators without needing a library of a priori selected operators. We…
TreeDOX predicts chaotic systems without hyperparameter tuning.
The well-known Mori-Zwanzig theory tells us that model reduction leads to memory effect. For a long time, modeling the memory effect accurately and efficiently has been an important but nearly impossible task in developing a good reduced model. In this work, we explore a natural analogy between recurrent neural network…
We use standard deep neural networks to classify univariate time series generated by discrete and continuous dynamical systems based on their chaotic or non-chaotic behaviour. Our approach to circumvent the lack of precise models for some of the most challenging real-life applications is to train different neural netwo…
Generative models speed up complex system simulations.
We develop a deep autoencoder architecture that can be used to find a coordinate transformation which turns a nonlinear PDE into a linear PDE. Our architecture is motivated by the linearizing transformations provided by the Cole-Hopf transform for Burgers equation and the inverse scattering transform for completely int…
A lightweight framework improves convergence and stability of PINNs for complex PDEs.
FiniteNet uses a neural network to improve PDE solving methods.
Develops theory for data-driven methods in dynamical systems.
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a useful data-driven approximation of the Koopman operator for analyzing dynamical syst…
A new method uses neural networks to improve POD-Galerkin models for complex systems.
Model reduction methods aim to describe complex dynamic phenomena using only relevant dynamical variables, decreasing computational cost, and potentially highlighting key dynamical mechanisms. In the absence of special dynamical features such as scale separation or symmetries, the time evolution of these variables typi…
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a multiscale description of the homological features within a dataset. A useful re…
Online algorithm identifies PDEs from noisy data snapshots.
Bayesian method learns PDEs from noisy data.
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In particular, we introduce \emph{hidden physics models}, which are essentially data-efficien…
In recent years, deep learning has proven to be a viable methodology for surrogate modeling and uncertainty quantification for a vast number of physical systems. However, in their traditional form, such models can require a large amount of training data. This is of particular importance for various engineering and scie…
A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical models of the physical world. In the current era of abundance of data and advan…
Novel autoencoder method approximates Koopman operator in low dimensions.
A new autoencoder combines deep learning with SVD to reduce model complexity.
New PINN formulation respects causality for complex systems.
Enhanced autoencoders improve ROMs for PDEs by capturing essential properties.
HFNO enhances interpretability of turbulent flows through parallel wavenumber bin processing.
Efficiently constructs sparse ROMs for high-dimensional data using causation entropy.
New EiV models correct bias in operator learning with noisy data.
Enhanced ensemble filters use machine learning to improve accuracy in filtering models.