20 citations · 40 across the 15 of their papers we have counts for
16 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…
A Mechanistic Analysis of Transformers for Dynamical Systems
Gregory Duthé, Nikolaos Evangelou, Wei Liu +2
Transformers are increasingly adopted for modeling and forecasting time-series, yet their internal mechanisms remain poorly understood from a dynamical systems perspective. In cont…
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 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…
Neural network-based singularity detection and applications
Nadiia Derevianko, Ioannis G. Kevrekidis, Felix Dietrich
We present a method for constructing a special type of shallow neural network that learns univariate meromorphic functions with pole-type singularities. Our method is based on usin…
Enabling Probabilistic Learning on Manifolds through Double Diffusion Maps
Dimitris G Giovanis, Nikolaos Evangelou, Ioannis G Kevrekidis +1
We present a generative learning framework for probabilistic sampling based on an extension of the Probabilistic Learning on Manifolds (PLoM) approach, which is designed to generat…
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…
Neural Chaos: A Spectral Stochastic Neural Operator
Bahador Bahmani, Ioannis G. Kevrekidis, Michael D. Shields
Building surrogate models with uncertainty quantification capabilities is essential for many engineering applications where randomness, such as variability in material properties,…
Comparing analytic and data-driven approaches to parameter identifiability: A power systems case study
Nikolaos Evangelou, Alexander M. Stankovic, Ioannis G. Kevrekidis +1
Parameter identifiability refers to the capability of accurately inferring the parameter values of a model from its observations (data). Traditional analysis methods exploit analyt…
A Resolution Independent Neural Operator
Bahador Bahmani, Somdatta Goswami, Ioannis G. Kevrekidis +1
The Deep Operator Network (DeepONet) is a powerful neural operator architecture that uses two neural networks to map between infinite-dimensional function spaces. This architecture…
On Learning what to Learn: heterogeneous observations of dynamics and establishing (possibly causal) relations among them
David W. Sroczynski, Felix Dietrich, Eleni D. Koronaki +4
Before we attempt to learn a function between two (sets of) observables of a physical process, we must first decide what the inputs and what the outputs of the desired function are…
RandONet: Shallow-Networks with Random Projections for learning linear and nonlinear operators
Gianluca Fabiani, Ioannis G. Kevrekidis, Constantinos Siettos +1
Deep Operator Networks (DeepOnets) have revolutionized the domain of scientific machine learning for the solution of the inverse problem for dynamical systems. However, their imple…
Integrating supervised and unsupervised learning approaches to unveil critical process inputs
Paris Papavasileiou, Dimitrios G. Giovanis, Gabriele Pozzetti +6
This study introduces a machine learning framework tailored to large-scale industrial processes characterized by a plethora of numerical and categorical inputs. The framework aims…
Nonlinear Manifold Learning Determines Microgel Size from Raman Spectroscopy
Eleni D. Koronaki, Luise F. Kaven, Johannes M. M. Faust +2
Polymer particle size constitutes a crucial characteristic of product quality in polymerization. Raman spectroscopy is an established and reliable process analytical technology for…
Coarse-grained computations of demixing in dense gas-fluidized beds
Sung Joon Moon, S. Sundaresan, I. G. Kevrekidis
We use an "equation-free", coarse-grained computational approach to accelerate molecular dynamics-based computations of demixing (segregation) of dissimilar particles subject to an…