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05/25/2023
Transporting Densities Across Dimensions
Even the best scientific equipment can only partially observe reality. R...
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05/05/2023
Data-driven and Physics Informed Modelling of Chinese Hamster Ovary Cell Bioreactors
Fed-batch culture is an established operation mode for the production of...
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04/27/2023
Some of the variables, some of the parameters, some of the times, with some physics known: Identification with partial information
Experimental data is often comprised of variables measured independently...
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03/31/2023
Implementation and (Inverse Modified) Error Analysis for implicitly-templated ODE-nets
We focus on learning unknown dynamics from data using ODE-nets templated...
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03/15/2023
Discrete-Time Nonlinear Feedback Linearization via Physics-Informed Machine Learning
We present a physics-informed machine learning (PIML) scheme for the fee...
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02/17/2023
On Equivalent Optimization of Machine Learning Methods
At the core of many machine learning methods resides an iterative optimi...
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02/09/2023
Gentlest ascent dynamics on manifolds defined by adaptively sampled point-clouds
Finding saddle points of dynamical systems is an important problem in pr...
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01/29/2023
Physics-agnostic and Physics-infused machine learning for thin films flows: modeling, and predictions from small data
Numerical simulations of multiphase flows are crucial in numerous engine...
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01/27/2023
Certified Invertibility in Neural Networks via Mixed-Integer Programming
Neural networks are notoriously vulnerable to adversarial attacks – smal...
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01/27/2023
From partial data to out-of-sample parameter and observation estimation with Diffusion Maps and Geometric Harmonics
A data-driven framework is presented, that enables the prediction of qua...
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11/22/2022
A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithms
Meta-learning of numerical algorithms for a given task consist of the da...
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10/28/2022
Two novel families of multiscale staggered patch schemes efficiently simulate large-scale, weakly damped, linear waves
Many multiscale wave systems exhibit macroscale emergent behaviour, for ...
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09/14/2022
Algorithmic (Semi-)Conjugacy via Koopman Operator Theory
Iterative algorithms are of utmost importance in decision and control. W...
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08/23/2022
Limits of Entrainment of Circadian Neuronal Networks
Circadian rhythmicity lies at the center of various important physiologi...
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08/23/2022
GANs and Closures: Micro-Macro Consistency in Multiscale Modeling
Sampling the phase space of molecular systems – and, more generally, of ...
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07/26/2022
Staggered grids for multidimensional multiscale modelling
Numerical schemes for wave-like systems with small dissipation are often...
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07/12/2022
Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach
We present an Equation/Variable free machine learning (EVFML) framework ...
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07/08/2022
Black and Gray Box Learning of Amplitude Equations: Application to Phase Field Systems
We present a data-driven approach to learning surrogate models for ampli...
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05/26/2022
Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data
We propose a machine learning framework for the data-driven discovery of...
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04/26/2022
Double Diffusion Maps and their Latent Harmonics for Scientific Computations in Latent Space
We introduce a data-driven approach to building reduced dynamical models...
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04/21/2022
Staying the course: Locating equilibria of dynamical systems on Riemannian manifolds defined by point-clouds
We introduce a method to successively locate equilibria (steady states) ...
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10/28/2021
An Operator Theoretic Perspective on Pruning Deep Neural Networks
The discovery of sparse subnetworks that are able to perform as well as ...
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10/13/2021
On the Parameter Combinations That Matter and on Those That do Not
We present a data-driven approach to characterizing nonidentifiability o...
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10/05/2021
On the Correspondence between Gaussian Processes and Geometric Harmonics
We discuss the correspondence between Gaussian process regression and Ge...
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07/29/2021
Learning the temporal evolution of multivariate densities via normalizing flows
In this work, we propose a method to learn probability distributions usi...
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05/04/2021
Personalized Algorithm Generation: A Case Study in Meta-Learning ODE Integrators
We study the meta-learning of numerical algorithms for scientific comput...
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04/27/2021
Initializing LSTM internal states via manifold learning
We present an approach, based on learning an intrinsic data manifold, fo...
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03/13/2021
Helmholtzian Eigenmap: Topological feature discovery edge flow learning from point cloud data
The manifold Helmholtzian (1-Laplacian) operator Δ_1 elegantly generaliz...
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12/23/2020
Learning emergent PDEs in a learned emergent space
We extract data-driven, intrinsic spatial coordinates from observations ...
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12/05/2020
Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks
We propose the Poisson neural networks (PNNs) to learn Poisson systems a...
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08/24/2020
Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations
The data-driven discovery of partial differential equations (PDEs) consi...
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07/10/2020
Transformations between deep neural networks
We propose to test, and when possible establish, an equivalence between ...
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04/15/2020
LOCA: LOcal Conformal Autoencoder for standardized data coordinates
We propose a deep-learning based method for obtaining standardized data ...
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04/13/2020
Emergent spaces for coupled oscillators
In this paper we present a systematic, data-driven approach to discoveri...
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04/09/2020
Spectral Discovery of Jointly Smooth Features for Multimodal Data
In this paper, we propose a spectral method for deriving functions that ...
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12/17/2019
Large-scale simulation of shallow water waves with computation only on small staggered patches
The multiscale patch scheme is built from given small micro-scale simula...
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09/12/2019
Coarse-scale PDEs from fine-scale observations via machine learning
Complex spatiotemporal dynamics of physicochemical processes are often m...
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07/25/2019
On the Koopman operator of algorithms
A systematic mathematical framework for the study of numerical algorithm...
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07/18/2019
A geometric approach to the transport of discontinuous densities
Different observations of a relation between inputs ("sources") and outp...
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06/03/2019
Optimal Transport on the Manifold of SPD Matrices for Domain Adaptation
The problem of domain adaptation has become central in many applications...
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01/31/2019
Transport map accelerated adaptive importance sampling, and application to inverse problems arising from multiscale stochastic reaction networks
In many applications, Bayesian inverse problems can give rise to probabi...
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12/16/2018
