no code implementations • 13 Mar 2024 • Eleni D. Koronaki, Luise F. Kaven, Johannes M. M. Faust, Ioannis G. Kevrekidis, Alexander Mitsos
Polymer particle size constitutes a crucial characteristic of product quality in polymerization.
no code implementations • 19 Feb 2024 • Hector Vargas Alvarez, Gianluca Fabiani, Ioannis G. Kevrekidis, Nikolaos Kazantzis, Constantinos Siettos
We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time nonlinear observer state estimation problem.
no code implementations • 30 Jan 2024 • Dimitris G. Giovanis, Dimitrios Loukrezis, Ioannis G. Kevrekidis, Michael D. Shields
To this end, we employ Principal Geodesic Analysis on the Grassmann manifold of the response to identify a set of disjoint principal geodesic submanifolds, of possibly different dimension, that captures the variation in the data.
1 code implementation • 21 Dec 2023 • Mario De Florio, Ioannis G. Kevrekidis, George Em Karniadakis
The performance of this framework is validated by recovering the right-hand sides and unknown terms of certain complex, chaotic systems such as the well-known Lorenz system, a six-dimensional hyperchaotic system, and the non-autonomous Sprott chaotic system, and comparing them with their known analytical expressions.
no code implementations • 20 Dec 2023 • Erez Peterfreund, Iryna Burak, Ofir Lindenbaum, Jim Gimlett, Felix Dietrich, Ronald R. Coifman, Ioannis G. Kevrekidis
Fusing measurements from multiple, heterogeneous, partial sources, observing a common object or process, poses challenges due to the increasing availability of numbers and types of sensors.
no code implementations • 10 Dec 2023 • Ellis R. Crabtree, Juan M. Bello-Rivas, Ioannis G. Kevrekidis
A valuable step in the modeling of multiscale dynamical systems in fields such as computational chemistry, biology, materials science and more, is the representative sampling of the phase space over long timescales of interest; this task is not, however, without challenges.
no code implementations • 1 Nov 2023 • Nikolaos Evangelou, Tianqi Cui, Juan M. Bello-Rivas, Alexei Makeev, Ioannis G. Kevrekidis
We study the tipping point collective dynamics of an adaptive susceptible-infected-susceptible (SIS) epidemiological network in a data-driven, machine learning-assisted manner.
no code implementations • 29 Oct 2023 • Nikolaos Evangelou, Dimitrios G. Giovanis, George A. Kevrekidis, Grigorios A. Pavliotis, Ioannis G. Kevrekidis
Deriving closed-form, analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs).
no code implementations • 24 Oct 2023 • Eleni D. Koronaki, Nikolaos Evangelou, Cristina P. Martin-Linares, Edriss S. Titi, Ioannis G. Kevrekidis
Both Black-Box and (theoretically-informed and data-corrected) Gray-Box models are described; the necessity for the latter arises when truncated Galerkin projections are so inaccurate as to not be amenable to post-processing.
no code implementations • 25 Sep 2023 • Gianluca Fabiani, Nikolaos Evangelou, Tianqi Cui, Juan M. Bello-Rivas, Cristina P. Martin-Linares, Constantinos Siettos, Ioannis G. Kevrekidis
We present a machine learning (ML)-assisted framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale modeling, for (a) detecting tipping points in the emergent behavior of complex systems, and (b) characterizing probabilities of rare events (here, catastrophic shifts) near them.
no code implementations • 5 May 2023 • Tianqi Cui, Tom S. Bertalan, Nelson Ndahiro, Pratik Khare, Michael Betenbaugh, Costas Maranas, Ioannis G. Kevrekidis
Fed-batch culture is an established operation mode for the production of biologics using mammalian cell cultures.
no code implementations • 27 Apr 2023 • Saurabh Malani, Tom S. Bertalan, Tianqi Cui, Jose L. Avalos, Michael Betenbaugh, Ioannis G. Kevrekidis
Iterates of such neural-network models allow for learning from data sampled at arbitrary time points $\textit{without}$ data modification.
no code implementations • 31 Mar 2023 • Aiqing Zhu, Tom Bertalan, Beibei Zhu, Yifa Tang, Ioannis G. Kevrekidis
We thus formulate an adaptive algorithm which monitors the level of error and adapts the number of (unrolled) implicit solution iterations during the training process, so that the error of the unrolled approximation is less than the current learning loss.
no code implementations • 15 Mar 2023 • Hector Vargas Alvarez, Gianluca Fabiani, Nikolaos Kazantzis, Constantinos Siettos, Ioannis G. Kevrekidis
We assess the performance of the proposed PIML approach via a benchmark nonlinear discrete map for which the feedback linearization transformation law can be derived analytically; the example is characterized by steep gradients, due to the presence of singularities, in the domain of interest.
no code implementations • 17 Feb 2023 • William T. Redman, Juan M. Bello-Rivas, Maria Fonoberova, Ryan Mohr, Ioannis G. Kevrekidis, Igor Mezić
Our data-driven approach is general and can be utilized broadly to compare the optimization of machine learning methods.
1 code implementation • 9 Feb 2023 • Juan M. Bello-Rivas, Anastasia Georgiou, Hannes Vandecasteele, Ioannis G. Kevrekidis
Finding saddle points of dynamical systems is an important problem in practical applications such as the study of rare events of molecular systems.
no code implementations • 27 Jan 2023 • Tianqi Cui, Thomas Bertalan, George J. Pappas, Manfred Morari, Ioannis G. Kevrekidis, Mahyar Fazlyab
Neural networks are known to be vulnerable to adversarial attacks, which are small, imperceptible perturbations that can significantly alter the network's output.
no code implementations • 22 Nov 2022 • Danimir T. Doncevic, Alexander Mitsos, Yue Guo, Qianxiao Li, Felix Dietrich, Manuel Dahmen, Ioannis G. Kevrekidis
Meta-learning of numerical algorithms for a given task consists of the data-driven identification and adaptation of an algorithmic structure and the associated hyperparameters.
no code implementations • 25 Aug 2022 • Yorgos M. Psarellis, Seungjoon Lee, Tapomoy Bhattacharjee, Sujit S. Datta, Juan M. Bello-Rivas, Ioannis G. Kevrekidis
The resulting data-driven PDE can then be simulated to reproduce/predict computational or experimental bacterial density profile data, and estimate the underlying (unmeasured) chemonutrient field evolution.
no code implementations • 23 Aug 2022 • Yorgos M. Psarellis, Michail Kavousanakis, Michael A. Henson, Ioannis G. Kevrekidis
In this work, we study a modern computational neuroscience model to determine the limits of circadian synchronization to external light signals of different frequency and duty cycle.
no code implementations • 23 Aug 2022 • Ellis R. Crabtree, Juan M. Bello-Rivas, Andrew L. Ferguson, Ioannis G. Kevrekidis
In this work, we present an approach that couples physics-based simulations and biasing methods for sampling conditional distributions with ML-based conditional generative adversarial networks for the same task.
no code implementations • 12 Jul 2022 • Dimitrios G. Patsatzis, Lucia Russo, Ioannis G. Kevrekidis, Constantinos Siettos
We present an Equation/Variable free machine learning (EVFML) framework for the control of the collective dynamics of complex/multiscale systems modelled via microscopic/agent-based simulators.
no code implementations • 8 Jul 2022 • Felix P. Kemeth, Sergio Alonso, Blas Echebarria, Ted Moldenhawer, Carsten Beta, Ioannis G. Kevrekidis
In these regimes, going beyond black-box identification, we explore different approaches to learn data-driven corrections to the analytically approximate models, leading to effective gray box partial differential equations.
no code implementations • 26 May 2022 • Seungjoon Lee, Yorgos M. Psarellis, Constantinos I. Siettos, Ioannis G. Kevrekidis
We exploit Automatic Relevance Determination (ARD) within a Gaussian Process framework for the identification of a parsimonious set of collective observables that parametrize the law of the effective PDEs.
1 code implementation • 30 Apr 2022 • Nikolaos Evangelou, Felix Dietrich, Juan M. Bello-Rivas, Alex Yeh, Rachel Stein, Michael A. Bevan, Ioannis G. Kevrekidis
We construct a reduced, data-driven, parameter dependent effective Stochastic Differential Equation (eSDE) for electric-field mediated colloidal crystallization using data obtained from Brownian Dynamics Simulations.
no code implementations • 26 Apr 2022 • Nikolaos Evangelou, Felix Dietrich, Eliodoro Chiavazzo, Daniel Lehmberg, Marina Meila, Ioannis G. Kevrekidis
A second round of Diffusion Maps on those latent coordinates allows the approximation of the reduced dynamical models.
1 code implementation • 21 Apr 2022 • Juan M. Bello-Rivas, Anastasia Georgiou, John Guckenheimer, Ioannis G. Kevrekidis
As in the Euclidean case, generalized isoclines of generic vector fields $X$ are smooth curves that connect equilibria of $X$.
no code implementations • 7 Feb 2022 • Erez Peterfreund, Ioannis G. Kevrekidis, Ariel Jaffe
Inferring the location of a mobile device in an indoor setting is an open problem of utmost significance.
no code implementations • ICLR 2022 • William T. Redman, Maria Fonoberova, Ryan Mohr, Ioannis G. Kevrekidis, Igor Mezic
The discovery of sparse subnetworks that are able to perform as well as full models has found broad applied and theoretical interest.
no code implementations • 13 Oct 2021 • Nikolaos Evangelou, Noah J. Wichrowski, George A. Kevrekidis, Felix Dietrich, Mahdi Kooshkbaghi, Sarah McFann, Ioannis G. Kevrekidis
We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models.
no code implementations • 5 Oct 2021 • Felix Dietrich, Juan M. Bello-Rivas, Ioannis G. Kevrekidis
We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts.
no code implementations • 29 Jul 2021 • Yubin Lu, Romit Maulik, Ting Gao, Felix Dietrich, Ioannis G. Kevrekidis, Jinqiao Duan
Specifically, the learned map is a multivariate normalizing flow that deforms the support of the reference density to the support of each and every density snapshot in time.
2 code implementations • 10 Jun 2021 • Felix Dietrich, Alexei Makeev, George Kevrekidis, Nikolaos Evangelou, Tom Bertalan, Sebastian Reich, Ioannis G. Kevrekidis
We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surrogate models of the fine scale dynamics.
2 code implementations • 4 May 2021 • Yue Guo, Felix Dietrich, Tom Bertalan, Danimir T. Doncevic, Manuel Dahmen, Ioannis G. Kevrekidis, Qianxiao Li
As a case study, we develop a machine learning approach that automatically learns effective solvers for initial value problems in the form of ordinary differential equations (ODEs), based on the Runge-Kutta (RK) integrator architecture.
no code implementations • 27 Apr 2021 • Felix P. Kemeth, Tom Bertalan, Nikolaos Evangelou, Tianqi Cui, Saurabh Malani, Ioannis G. Kevrekidis
We present an approach, based on learning an intrinsic data manifold, for the initialization of the internal state values of LSTM recurrent neural networks, ensuring consistency with the initial observed input data.
no code implementations • 13 Mar 2021 • Yu-Chia Chen, Weicheng Wu, Marina Meilă, Ioannis G. Kevrekidis
In this work, we propose the estimation of the manifold Helmholtzian from point cloud data by a weighted 1-Laplacian $\mathcal L_1$.
no code implementations • 23 Dec 2020 • Felix P. Kemeth, Tom Bertalan, Thomas Thiem, Felix Dietrich, Sung Joon Moon, Carlo R. Laing, Ioannis G. Kevrekidis
These coordinates then serve as an emergent space in which to learn predictive models in the form of partial differential equations (PDEs) for the collective description of the coupled-agent system.
1 code implementation • 5 Dec 2020 • Pengzhan Jin, Zhen Zhang, Ioannis G. Kevrekidis, George Em Karniadakis
We propose the Poisson neural networks (PNNs) to learn Poisson systems and trajectories of autonomous systems from data.
1 code implementation • 24 Aug 2020 • Hassan Arbabi, Judith E. Bunder, Giovanni Samaey, Anthony J. Roberts, Ioannis G. Kevrekidis
Training deep neural networks to learn such data-driven partial differential operators requires extensive spatiotemporal data.
Numerical Analysis Numerical Analysis Computational Physics 35B27
no code implementations • 10 Jul 2020 • Tom Bertalan, Felix Dietrich, Ioannis G. Kevrekidis
We propose to test, and when possible establish, an equivalence between two different artificial neural networks by attempting to construct a data-driven transformation between them, using manifold-learning techniques.
no code implementations • 15 Apr 2020 • Erez Peterfreund, Ofir Lindenbaum, Felix Dietrich, Tom Bertalan, Matan Gavish, Ioannis G. Kevrekidis, Ronald R. Coifman
We propose a deep-learning based method for obtaining standardized data coordinates from scientific measurements. Data observations are modeled as samples from an unknown, non-linear deformation of an underlying Riemannian manifold, which is parametrized by a few normalized latent variables.
no code implementations • 9 Apr 2020 • Felix Dietrich, Or Yair, Rotem Mulayoff, Ronen Talmon, Ioannis G. Kevrekidis
We show analytically that our method is guaranteed to provide a set of orthogonal functions that are as jointly smooth as possible, ordered by increasing Dirichlet energy from the smoothest to the least smooth.
no code implementations • 12 Sep 2019 • Seungjoon Lee, Mahdi Kooshkbaghi, Konstantinos Spiliotis, Constantinos I. Siettos, Ioannis G. Kevrekidis
In this paper, we introduce a data-driven framework for the identification of unavailable coarse-scale PDEs from microscopic observations via machine learning algorithms.
no code implementations • 3 Jun 2019 • Or Yair, Felix Dietrich, Ronen Talmon, Ioannis G. Kevrekidis
We model the difference between two domains by a diffeomorphism and use the polar factorization theorem to claim that OT is indeed optimal for DA in a well-defined sense, up to a volume preserving map.
no code implementations • 16 Dec 2018 • Seungjoon Lee, Felix Dietrich, George E. Karniadakis, Ioannis G. Kevrekidis
In this paper, we will explore mathematical algorithms for multifidelity information fusion that use such an approach towards improving the representation of the high-fidelity function with only a few training data points.
no code implementations • 16 Oct 2016 • Oliver Junge, Ioannis G. Kevrekidis
We propose to compute approximations to general invariant sets in dynamical systems by minimizing the distance between an appropriately selected finite set of points and its image under the dynamics.
Dynamical Systems Chaotic Dynamics