Publications

hessQuik: Fast Hessian computation of composite functions

hessQuik is a lightweight pyTorch library for fast computation of second-order derivatives (Hessians) of composite functions (for example, deep neural networks) with respect to their inputs. The repository includes a variety of popular functions and layers, including residual layers and input convex layers, from which users can build complex models through composition.
Elizabeth Newman, Lars Ruthotto
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A Neural Network Approach for High-Dimensional Optimal Control Applied to Multi-Agent Path Finding

We propose a neural network approach that yields approximate solutions for high-dimensional optimal control problems and demonstrate …
Derek Onken, Levon Nurbekyan, Xingjian Li, Samy Wu Fung, Stanley Osher, Lars Ruthotto
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Multivariate Quantile Function Forecaster

We propose Multivariate Quantile Function Forecaster (MQF2), a global probabilistic forecasting method constructed using a multivariate …
Kelvin Kan, François-Xavier Aubet, Tim Januschowski, Youngsuk Park, Konstantinos Benidis, Lars Ruthotto, Jan Gasthaus
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slimTrain - A Stochastic Approximation Method for Training Separable Deep Neural Networks

Deep neural networks (DNNs) have shown their success as high-dimensional function approximators in many applications; however, training …
Elizabeth Newman, Julianne Chung, Matthias Chung, Lars Ruthotto
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Train Like a (Var)Pro: Efficient Training of Neural Networks with Variable Projection

Deep neural networks (DNNs) have achieved state-of-the-art performance across a variety of tradi- tional machine learning tasks, e.g., …
Elizabeth Newman, Lars Ruthotto, Joseph Hart, Bart van Bloemen Waanders
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Train Like a (Var)Pro: Efficient Training of Neural Networks with Variable Projection

PNKH-B: A Projected Newton-Krylov Method for Large-Scale Bound-Constrained Optimization

We present PNKH-B, a projected Newton-Krylov method with a low-rank approximated Hessian metric for approximately solving large-scale …
Kelvin Kan, Samy Wu Fung, Lars Ruthotto
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An Introduction to Deep Generative Modeling

Deep generative models (DGM) are neural networks with many hidden layers trained to approximate complicated, high-dimensional …
Lars Ruthotto, Eldad Haber
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New Bridges Between Deep Learning and Partial Differential Equations

Understanding the world through data and computation has always formed the core of scientific discovery. Amid many different …
Lars Ruthotto
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Avoiding The Double Descent Phenomenon of Random Feature Models Using Hybrid Regularization

We demonstrate the ability of hybrid regularization methods to automatically avoid the double descent phenomenon arising in the …
Kelvin Kan, James G Nagy, Lars Ruthotto
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A Neural Network Approach Applied to Multi-Agent Optimal Control

We propose a neural network approach for solving high-dimensional optimal control problems. In particular, we focus on multi-agent …
Derek Onken, Levon Nurbekyan, Xingjian Li, Samy Wu Fung, Stanley Osher, Lars Ruthotto
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OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transport

A normalizing flow is an invertible mapping between an arbitrary probability distribution and a standard normal distribution; it can be …
Derek Onken, Samy Wu Fung, Xingjian Li, Lars Ruthotto
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Discretize-Optimize vs. Optimize-Discretize for Time-Series Regression and Continuous Normalizing Flows

We compare the discretize-optimize (Disc-Opt) and optimize-discretize (Opt-Disc) approaches for time-series regression and continuous …
Derek Onken, Lars Ruthotto
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LeanConvNets: Low-cost Yet Effective Convolutional Neural Networks

Convolutional Neural Networks (CNNs) have be- come indispensable for solving machine learning tasks in speech recognition, computer …
Jonathan Ephrath, Moshe Eliasof, Lars Ruthotto, Eldad Haber, Eran Treister
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Layer-Parallel Training of Deep Residual Neural Networks

Residual neural networks (ResNets) are a promising class of deep neural networks that have shown excellent performance for a number of …
Stefanie Günther, Lars Ruthotto, Jacob B Schroder, Eric C Cyr, Nicolas R Gauger
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Gauss–Newton Optimization for Phase Recovery From the Bispectrum

Phase recovery from the bispectrum is a central problem in speckle interferometry which can be posed as an optimization problem …
James Lincoln Herring, James Nagy, Lars Ruthotto
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Deep neural networks motivated by partial differential equations

Partial differential equations (PDEs) are in- dispensable for modeling many physical phenomena and also commonly used for solving image …
Lars Ruthotto, Eldad Haber
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ADMM-Softmax: an ADMM approach for multinomial logistic regression

We present ADMM-Softmax, an alternating direction method of multipliers (ADMM) for solving multinomial logistic regression (MLR) …
Samy Wu Fung, Sanna Tyrväinen, Lars Ruthotto, Eldad Haber
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A machine learning framework for solving high-dimensional mean field game and mean field control problems

Mean field games (MFG) and mean field control (MFC) are critical classes of multiagent models for the efficient analysis of massive …
Lars Ruthotto, Stanley J Osher, Wuchen Li, Levon Nurbekyan, Samy Wu Fung
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A machine learning framework for solving high-dimensional mean field game and mean field control problems

hMRI - A toolbox for quantitative MRI in neuroscience and clinical research

Neuroscience and clinical researchers are increasingly interested in quantitative magnetic resonance imaging (qMRI) due to its …
Karsten Tabelow, Evelyne Balteau, John Ashburner, Martina F Callaghan, Bogdan Draganski, Gunther Helms, Ferath Kherif, Tobias Leutritz, Antoine Lutti, Christophe Phillips, Enrico Reimer, Lars Ruthotto, Maryam Seif, Nikolaus Weiskopf, Gabriel Ziegler, Siawoosh Mohammadi
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LeanResNet: A Low-cost yet Effective Convolutional Residual Networks

Convolutional Neural Networks (CNNs) filter the input data using a series of spatial convolution operators with compact stencils and …
Jonathan Ephrath, Lars Ruthotto, Eldad Haber, Eran Treister
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IMEXnet: A Forward Stable Deep Neural Network

Deep convolutional neural networks have revolutionized many machine learning and computer vision tasks, however, some remaining key …
Eldad Haber, Keegan Lensink, Eran Treister, Lars Ruthotto
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An Uncertainty-Weighted Asynchronous ADMM Method for Parallel PDE Parameter Estimation

We consider a global variable consensus ADMM algorithm for solving large-scale PDE parameter estimation problems asynchronously and in …
Samy Wu Fung, Lars Ruthotto
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A Multiscale Method for Model Order Reduction in PDE Parameter Estimation

Estimating parameters of Partial Differential Equations (PDEs) is of interest in a number of applications such as geophysical and …
Samy Wu Fung, Lars Ruthotto
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A Bayesian framework for molecular strain identification from mixed diagnostic samples

We provide a mathematical formulation and develop a computational framework for identifying multiple strains of microorganisms from …
Lauri Mustonen, Xiangxi Gao, Asteroide Santana, Rebecca Mitchell, Ymir Vigfusson, Lars Ruthotto
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Never look back - A modified EnKF method and its application to the training of neural networks without back propagation

In this work, we present a new derivative-free optimization method and investigate its use for training neural networks. Our method is …
Eldad Haber, Felix Lucka, Lars Ruthotto
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Low-Cost Parameterizations of Deep Convolutional Neural Networks

Convolutional Neural Networks (CNNs) filter the input data using a series of spatial convolution operators with compactly supported …
Eran Treister, Lars Ruthotto, Michal Sharoni, Sapir Zafrani, Eldad Haber
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Reversible architectures for arbitrarily deep residual neural networks

Recently, deep residual networks have been successfully applied in many computer vision and natural language processing tasks, pushing …
Bo Chang, Lili Meng, Eldad Haber, Lars Ruthotto, David Begert, Elliot Holtham
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Optimal Experimental Design for Inverse Problems with State Constraints

In this paper, we address the challenging problem of optimal experimental design (OED) of inverse problems with state constraints. We …
Lars Ruthotto, Julianne Chung, Matthias Chung
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Stable architectures for deep neural networks

Deep neural networks have become invaluable tools for supervised machine learning, e.g. classification of text or images. While often …
Eldad Haber, Lars Ruthotto
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Stable architectures for deep neural networks

Numerical Methods for Polyline-to-Point-Cloud Registration with Applications to Patient-Specific Stent Reconstruction

We present novel numerical methods for polyline‐to‐point‐cloud registration and their application to patient‐specific modeling of …
Claire Y Lin, Alessandro Veneziani, Lars Ruthotto

Learning across scales - A multiscale method for Convolution Neural Networks

In this work we establish the relation between optimal control and training deep Convolution Neural Networks (CNNs). We show that the …
Eldad Haber, Lars Ruthotto, Elliot Holtham, Seong-Hwan Jun
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LAP: a Linearize and Project Method for Solving Inverse Problems with Coupled Variables

Many inverse problems involve two or more sets of variables that represent different physical quantities but are tightly coupled with …
James L Herring, James G Nagy, Lars Ruthotto
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jInv - a Flexible Julia Package for PDE Parameter Estimation

Estimating parameters of Partial Differential Equations (PDEs) from noisy and indirect measurements requires solutions of ill-posed …
Lars Ruthotto, Eran Treister, Eldad Haber
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Improved Susceptibility Artifact Correction of Echo Planar MRI using the Alternating Direction Method of Multipliers

We present an improved technique for susceptibility artifact correction in echo-planar imaging (EPI), a widely used ultra-fast magnetic …
Jan Macdonald, Lars Ruthotto
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A Stabilized Multigrid Solver for Hyperelastic Image Registration

Image registration is a central problem in a variety of areas involving imaging techniques, and is known to be challenging and …
Lars Ruthotto, Chen Greif, Jan Modersitzki
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A Lagrangian Gauss-Newton-Krylov Solver for Mass- and Intensity-Preserving Diffeomorphic Image Registration

We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic …
Andreas Mang, Lars Ruthotto
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Efficient Numerical Optimization For Susceptibility Artifact Correction Of EPI-MRI

We present two efficient numerical methods for susceptibility artifact correction in Echo Planar Imaging (EPI), an ultra fast Magnetic …
Jan Macdonald, Lars Ruthotto
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Computational methods for image reconstruction

Reconstructing images from indirect measurements is a central problem in many applications, including the subject of this special …
J Chung, Lars Ruthotto
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Combined Background Field Removal and Reconstruction for Quantitative Susceptibility Mapping

Maximilian März, Lars Ruthotto
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Non-linear Image Registration

Image registration is to automatically establish geometrical correspondences between two images. It is an essential task in almost all …
Lars Ruthotto, Jan Modersitzki
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A multiscale finite volume method for Maxwell's equations at low frequencies

Eldad Haber, Lars Ruthotto

Model-based parameter estimation in DCE-MRI without an Arterial Input Function

Analysis of DCE-MRI data is often carried out by fitting parametric models. However, one major factor of uncertainty is the …
Constantin Heck, Lars Ruthotto, Jan Modersitzki, Benjamin Berkels
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High-resolution diffusion kurtosis imaging at 3T enabled by advanced post-processing.

Diffusion Kurtosis Imaging (DKI) is more sensitive to microstructural differences and can be related to more specific micro-scale …
Siawoosh Mohammadi, Karsten Tabelow, Lars Ruthotto, Thorsten Feiweier, Jörg Polzehl, Nikolaus Weiskopf

Geophysical Imaging of Fluid Flow in Porous Media

Imaging and prediction of fluid flow in the subsurface provides information that is crucial for decision making processes in fields …
Jennifer Fohring, Eldad Haber, Lars Ruthotto
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A New Method for Joint Susceptibility Artefact Correction and Super-Resolution for dMRI

Diffusion magnetic resonance imaging (dMRI) has become increasingly relevant in clinical research and neuroscience. It is commonly …
Lars Ruthotto, Siawoosh Mohammadi, Nikolaus Weiskopf
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Hyperelastic Susceptibility Artifact Correction of DTI in SPM

Echo Planar Imaging (EPI) is a MRI acquisition technique that is the backbone of widely used investigation techniques in neuroscience …
Lars Ruthotto, Siawoosh Mohammadi, Constantin Heck, Jan Modersitzki, Nikolaus Weiskopf
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A Hyperelastic Regularization Energy for Image Registration

Image registration is one of the most challenging problems in image processing, where ill-posedness arises due to noisy data as well as …
Martin Burger, Jan Modersitzki, Lars Ruthotto
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A Hyperelastic Regularization Energy for Image Registration

Diffeomorphic susceptibility artifact correction of diffusion-weighted magnetic resonance images

Diffusion-weighted magnetic resonance imaging is a key investigation technique in modern neuroscience. In clinical settings, …
Lars Ruthotto, H Kugel, J Olesch, B Fischer, J Modersitzki, M Burger, C H Wolters
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Motion Correction in Dual Gated Cardiac PET Using Mass-Preserving Image Registration

Respiratory and cardiac motion leads to image degradation in positron emission tomography (PET) studies of the human heart. In this …
Fabian Gigengack, Lars Ruthotto, Martin Burger, Carsten H Wolters, Xiaoyi Jiang, Klaus P Schäfers
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Registration of Dynamic Contrast Enhanced MRI with Local Rigidity Constraint

Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) of the kidney provides important information for the diagnosis of renal …
Lars Ruthotto, Erlend Hodneland, Jan Modersitzki
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A Simplified Pipeline for Motion Correction in Dual Gated Cardiac PET

Positron Emission Tomography (PET) is a nuclear imaging technique of increasing importance e.g. in cardiovascular investigations. …
Lars Ruthotto, Fabian Gigengack, Martin Burger, Carsten H Wolters, Xiaoyi Jiang, Klaus P Schäfers, Jan Modersitzki
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A variational approach for the correction of field-inhomogeneities in EPI sequences

A wide range of medical applications in clinic and research exploit images acquired by fast magnetic resonance imaging (MRI) sequences …
Janine Olesch, Lars Ruthotto, Harald Kugel, Stefan Skare, Bernd Fischer, Carsten H Wolters
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Mass-preserving registration of medical images

Lars Ruthotto