10 papers
Generative Learning of Separatrices
Ellis R. Crabtree, Dimitris G. Giovanis, Anastasia Georgiou +2
The identification and reconstruction of the boundaries separating basins of attraction in multistable, multidimensional dynamical systems presents a fundamental challenge in compu…
Singularities in Multi-Objective Optimization and their Crossing during Continuation
Arjun Manoj, Michail E. Kavousanakis, Shanqing Liu +1
Continuation methods help trace Pareto sets in multi-objective optimization but are inherently local: a single run traces a single connected branch, requiring multiple restarts to…
BumpNet: A Sparse MLP Framework for Learning PDE Solutions
Shao-Ting Chiu, Ioannis G. Kevrekidis, Ulisses Braga-Neto
We introduce BumpNet, a sparse multilayer perceptron (MLP) framework for PDE numerical solution and operator learning. BumpNet is based on basis function expansion, which makes the…
A Mechanistic Analysis of Transformers for Dynamical Systems
Gregory Duthé, Gregory Duthé, Nikolaos Evangelou +3
Transformers are increasingly adopted for modeling and forecasting time-series, yet their internal mechanisms remain poorly understood from a dynamical systems perspective. In cont…
A Physics-informed Multi-resolution Neural Operator
Sumanta Roy, Bahador Bahmani, Ioannis G. Kevrekidis +1
The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial am…
Enabling Local Neural Operators to perform Equation-Free System-Level Analysis
Gianluca Fabiani, Hannes Vandecasteele, Somdatta Goswami +2
Neural Operators (NOs) provide a powerful framework for computations involving physical laws that can be modelled by (integro-) partial differential equations (PDEs), directly lear…