449 citations · 831 across the 30 of their papers we have counts for
32 papers
Rational neural networks for tracking complex singularities of nonlinear PDEs
Nadiia Derevianko, Hans-Joachim Bungartz, Felix Dietrich
We present a neural network-based method for numerical analytic continuation of solutions of nonlinear partial differential equations (PDEs) and detection of their complex singular…
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…
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…
Gappy local conformal auto-encoders for heterogeneous data fusion: in praise of rigidity
Erez Peterfreund, Iryna Burak, Ofir Lindenbaum +4
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…
Sampling weights of deep neural networks
Erik Lien Bolager, Iryna Burak, Chinmay Datar +2
We introduce a probability distribution, combined with an efficient sampling algorithm, for weights and biases of fully-connected neural networks. In a supervised learning context,…
Transporting Densities Across Dimensions
Michael Plainer, Felix Dietrich, Ioannis G. Kevrekidis
Even the best scientific equipment can only partially observe reality. Recorded data is often lower-dimensional, e.g., two-dimensional pictures of the three-dimensional world. Comb…
Data-driven modelling of brain activity using neural networks, Diffusion Maps, and the Koopman operator
Ioannis K. Gallos, Daniel Lehmberg, Felix Dietrich +1
We propose a machine-learning approach to model long-term out-of-sample dynamics of brain activity from task-dependent fMRI data. Our approach is a three stage one. First, we explo…
On the Use of Neural Networks for Full Waveform Inversion
Leon Herrmann, Tim Bürchner, Felix Dietrich +1
Neural networks have recently gained attention in solving inverse problems. One prominent methodology are Physics-Informed Neural Networks (PINNs) which can solve both forward and…
A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithms
Danimir T. Doncevic, Alexander Mitsos, Yue Guo +4
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. To…
Safe Policy Improvement Approaches and their Limitations
Philipp Scholl, Felix Dietrich, Clemens Otte +1
Safe Policy Improvement (SPI) is an important technique for offline reinforcement learning in safety critical applications as it improves the behavior policy with a high probabilit…
Learning Effective SDEs from Brownian Dynamics Simulations of Colloidal Particles
Nikolaos Evangelou, Felix Dietrich, Juan M. Bello-Rivas +4
We construct a reduced, data-driven, parameter dependent effective Stochastic Differential Equation (eSDE) for electric-field mediated colloidal crystallization using data obtained…
Double Diffusion Maps and their Latent Harmonics for Scientific Computations in Latent Space
Nikolaos Evangelou, Felix Dietrich, Eliodoro Chiavazzo +3
We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning…
Safe Policy Improvement Approaches on Discrete Markov Decision Processes
Philipp Scholl, Felix Dietrich, Clemens Otte +1
Safe Policy Improvement (SPI) aims at provable guarantees that a learned policy is at least approximately as good as a given baseline policy. Building on SPI with Soft Baseline Boo…
Quantum Process Tomography of Unitary Maps from Time-Delayed Measurements
Irene López Gutiérrez, Felix Dietrich, Christian B. Mendl
Quantum process tomography conventionally uses a multitude of initial quantum states and then performs state tomography on the process output. Here we propose and study an alternat…
On the Correspondence between Gaussian Processes and Geometric Harmonics
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. Research…
On the Parameter Combinations That Matter and on Those That do Not
Nikolaos Evangelou, Noah J. Wichrowski, George A. Kevrekidis +4
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. By employing Diff…
Learning the temporal evolution of multivariate densities via normalizing flows
Yubin Lu, Romit Maulik, Ting Gao +3
In this work, we propose a method to learn multivariate probability distributions using sample path data from stochastic differential equations. Specifically, we consider temporall…
Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learning
Felix Dietrich, Alexei Makeev, George Kevrekidis +4
We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surr…
Personalized Algorithm Generation: A Case Study in Learning ODE Integrators
Yue Guo, Felix Dietrich, Tom Bertalan +4
We study the learning of numerical algorithms for scientific computing, which combines mathematically driven, handcrafted design of general algorithm structure with a data-driven a…
Learning emergent PDEs in a learned emergent space
Felix P. Kemeth, Tom Bertalan, Thomas Thiem +4
We extract data-driven, intrinsic spatial coordinates from observations of the dynamics of large systems of coupled heterogeneous agents. These coordinates then serve as an emergen…
Transformations between deep neural networks
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 the…
LOCA: LOcal Conformal Autoencoder for standardized data coordinates
Erez Peterfreund, Ofir Lindenbaum, Felix Dietrich +4
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-linea…
Spectral Discovery of Jointly Smooth Features for Multimodal Data
Felix Dietrich, Or Yair, Rotem Mulayoff +2
In this paper, we propose a spectral method for deriving functions that are jointly smooth on multiple observed manifolds. This allows us to register measurements of the same pheno…
A geometric approach to the transport of discontinuous densities
Caroline Moosmüller, Felix Dietrich, Ioannis G. Kevrekidis
Different observations of a relation between inputs ("sources") and outputs ("targets") are often reported in terms of histograms (discretizations of the source and the target dens…