Related papers: Lie Transform--based Neural Networks for Dynamics …
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be…
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
We present a novel approach to modelling and learning vector fields from physical systems using neural networks that explicitly satisfy known linear operator constraints. To achieve this, the target function is modelled as a linear…
The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…
Deep learning has emerged as a powerful framework for analyzing biomolecular dynamics trajectories, enabling efficient representations that capture essential system dynamics and facilitate mechanistic studies. We propose a neural network…
Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend the method to partial differential equations. The resulting…
Simulating hair dynamics that generalize across arbitrary hairstyles, body shapes, and motions is a critical challenge. Our novel two-stage neural solution is the first to leverage Transformer-based architectures for such a broad…
Matrix reordering is a task to permute the rows and columns of a given observed matrix such that the resulting reordered matrix shows meaningful or interpretable structural patterns. Most existing matrix reordering techniques share the…
Deep neural networks come in many sizes and architectures. The choice of architecture, in conjunction with the dataset and learning algorithm, is commonly understood to affect the learned neural representations. Yet, recent results have…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
Using transformers over large generated datasets, we train models to learn mathematical properties of differential systems, such as local stability, behavior at infinity and controllability. We achieve near perfect prediction of qualitative…
We present a simple non-generative approach to deep representation learning that seeks equivariant deep embedding through simple objectives. In contrast to existing equivariant networks, our transformation coding approach does not constrain…
Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension $d$, with $d\leq 4$. We identify such a class by employing…
The paper develops a Transformer architecture for estimating dynamic factors from multivariate time series data under flexible identification assumptions. Performance on small datasets is improved substantially by using a conventional…
Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…
Most current neural networks for molecular dynamics (MD) include physical inductive biases, resulting in specialized and complex architectures. This is in contrast to most other machine learning domains, where specialist approaches are…
The use of deep neural network (DNN) models as surrogates for linear and nonlinear structural dynamical systems is explored. The goal is to develop DNN based surrogates to predict structural response, i.e., displacements and accelerations,…
Network traffic analysis is fundamental for network management, troubleshooting, and security. Tasks such as traffic classification, anomaly detection, and novelty discovery are fundamental for extracting operational information from…
Finding the Lie-algebraic closure of a handful of matrices has important applications in quantum computing and quantum control. For most realistic cases, the closure cannot be determined analytically, necessitating an explicit numerical…
There is a recent growing interest in applying Deep Learning techniques to tabular data, in order to replicate the success of other Artificial Intelligence areas in this structured domain. Specifically interesting is the case in which…