Research

In the past years, machine learning has started to help map, understand and predict the molecular biology of single cells. We develop methods that address specific biological hypotheses and originate from different areas of machine learning.

Before joining the field in 2015 as a postdoc with Fabian Theis, I developed computational techniques for predicting the emergent behavior of models of strongly correlated quantum materials, basic models of quantum computers, and chemical reactions in solar cells.

- Dynamical modeling of RNA velocity
- Generative modeling of single-cell perturbation effects
- Mapping the coarse-grained connectivity of complex manifolds
- Scalable and comprehensive software for single-cell analysis
- Interpretable knowledge-enriched latent representations of scRNA-seq
- Reconstructing cell cycle and disease progression using deep learning
- Deep-learning based diagnosis of lung cancer from images
- Solving dynamical mean-field theory using tensor trains
- Modeling diffusion-reaction chemistry of solar cells to improve conversion efficiency
- Dynamics of the quantum Rabi model
- Supercurrent through grain boundaries
- Coherent expansions of quantum matter and matter wave lasers
- Relaxation of a quantum many-body system after perturbation
- Sartre at Stammheim

The introduction of RNA velocity in single cells has opened up new ways of studying cellular differentiation in scRNA-seq [LaManno18]. It describes the rate of gene expression change for an individual gene at a given time point based on the ratio of its spliced and unspliced messenger RNA (mRNA). With scVelo, we solve the full transcriptional dynamics of splicing kinetics using a likelihood-based dynamical model. This generalizes RNA velocity to a wide variety of systems comprising transient cell states, which are common in development and in response to perturbations. The paper made it on the cover of Nature Biotechnology.

P28 Generalizing RNA velocity to transient cell states through dynamical modeling

V Bergen, M Lange, S Peidli,__FA Wolf†__, FJ Theis†

Nature Biotechnology (2020) cover story bioRxiv pdf code

V Bergen, M Lange, S Peidli,

Nature Biotechnology (2020) cover story bioRxiv pdf code

We showed that generative models are able to predict single-cell perturbation responses out-of-distribution [P27]. In principle, this approach should enable training models to predict the effects of disease and disease treatment across cell types and species. While the first implementation of the approach (scGen) relied on latent space vector arithmetics, we recently published an end-to-end-trained model based on a conditional variational autoencoder (trVAE) [P29] and a deep factor model [P32]. We wrote a review about the emerging field [P31].

P32 Compositional perturbation autoencoder for single-cell response modeling

M Lotfollahi*, A Klimovskaia*, CD Donno**, Y Ji**, IL Ibarra,__FA Wolf__, N Yakubova, FJ Theis†, D Lopez-Paz†

bioRxiv (2021) Facebook AI blog pdf code

M Lotfollahi*, A Klimovskaia*, CD Donno**, Y Ji**, IL Ibarra,

bioRxiv (2021) Facebook AI blog pdf code

P31 Machine learning for perturbational single-cell omics

Y Ji, M Lotfollahi,__FA Wolf__, FJ Theis

Cell Systems (2021) resource

Y Ji, M Lotfollahi,

Cell Systems (2021) resource

P29 Conditional out-of-distribution generation for unpaired data using transfer VAE

M Lotfollahi, M Naghipourfar, FJ Theis†,__FA Wolf†__

Bioinformatics (2020) talk at ECCB arXiv pdf code

M Lotfollahi, M Naghipourfar, FJ Theis†,

Bioinformatics (2020) talk at ECCB arXiv pdf code

P27 scGen predicts single-cell perturbation responses

M Lotfollahi,__FA Wolf†__, FJ Theis†

Nature Methods (2019) bioRxiv pdf code

M Lotfollahi,

Nature Methods (2019) bioRxiv pdf code

Partition-based graph abstraction (PAGA) aims to reconcile clustering with manifold learning by explaining variation using both discrete and continuous latent variables [P26]. PAGA generates coarse-grained maps of manifolds with complex topologies in a computationally efficient and robust way. In [P24], we used it to infer the first lineage tree of a whole complex animal - a Science breakthrough of the year 2018. It has been benchmarked as the overall best performing trajectory inference method in a review of ~70 methods by Saelens *et al.* (Nat. Biotechn., 2019) [tweet]. PAGA also builds on *diffusion pseudotime* [P19], which defined a robust global measure of similarity among cells.

P26 PAGA: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells

__FA Wolf__, F Hamey, M Plass, J Solana, JS Dahlin, B Göttgens, N Rajewsky, L Simon, FJ Theis

Genome Biology (2019) talk at SCG bioRxiv pdf code

Genome Biology (2019) talk at SCG bioRxiv pdf code

P24 Cell type atlas and lineage tree of a whole complex animal by single-cell transcriptomics

M Plass*, J Solana*,__FA Wolf__, S Ayoub, A Misios, P Glažar, B Obermayer, FJ Theis, C Kocks, N Rajewsky

Science (2018) pdf code

M Plass*, J Solana*,

Science (2018) pdf code

P19 Diffusion pseudotime robustly reconstructs branching cellular lineages

L Haghverdi, M Büttner,__FA Wolf__, F Buettner, FJ Theis

Nature Methods (2016) bioRxiv pdf

L Haghverdi, M Büttner,

Nature Methods (2016) bioRxiv pdf

Scanpy [P23] is a scalable toolkit for analyzing single-cell gene expression data. It includes preprocessing, visualization, clustering, trajectory inference and differential expression testing. Together with the underlying anndata it has become widely used and lead to a little ecosystem. It has been selected as an *Essential Open Source Software for Science* by CZI among 32 projects, alongside giants such as numpy, pandas, scikit-learn, matplotlib, and others. See software.

P23 Scanpy: large-scale single-cell gene expression data analysis

__FA Wolf__, P Angerer, FJ Theis

Genome Biology (2018) bioRxiv pdf code

Genome Biology (2018) bioRxiv pdf code

Existing methods for learning latent representations for single-cell RNA-seq data are based on autoencoders and factor models where the former are hard to interpret and the latter have limited flexibility. Here, we introduce a framework for learning interpretable autoencoders based on regularized linear decoders, decomposing variation into interpretable components using prior knowledge.

P30 Learning interpretable latent autoencoder representations with annotations of feature sets

S Rybakov, M Lotfollahi, FJ Theis†,__FA Wolf†__

Machine Learning in Computational Biology (2020) conference proceeding bioRxiv pdf code

S Rybakov, M Lotfollahi, FJ Theis†,

Machine Learning in Computational Biology (2020) conference proceeding bioRxiv pdf code

Using large-scale imaging data, we show how to reconstruct continuous biological processes using deep learning for the examples of cell cycle and disease progression in diabetic retinopathy [P20]. Read more.

P20 Reconstructing cell cycle and disease progression using deep learning

P Eulenberg*, N Köhler*, T Blasi, A Filby, AE Carpenter, P Rees, FJ Theis†,__FA Wolf†__

Nature Communications (2017) bioRxiv pdf code

P Eulenberg*, N Köhler*, T Blasi, A Filby, AE Carpenter, P Rees, FJ Theis†,

Nature Communications (2017) bioRxiv pdf code

The goal of the Data Science Bowl 2017 was to predict lung cancer from tomography scans. It was the highest endowed machine learning competition with $1M total in prize money in 2017. We won the 7th prize among nearly 2.4k teams and more than 10k participants; the best result among all German teams.

O7 Predicting cancer from three dimensional computer tomography scans of the lung

N Köhler, J Jungwirth, M Berthold,__FA Wolf__

Report (2017) pdf code

N Köhler, J Jungwirth, M Berthold,

Report (2017) pdf code

Tensor trains (MPS, DMRG) constitute - together with quantum monte carlo and the numerical renormalization group - the key numerical approach for tackling the exponential computational complexity of models of strongly correlated materials and quantum computers.

We developed a way to use tensor trains within dynamical mean-field theory to enabable the simulation of previously inaccessible emergent properties of strongly correlated materials [O6,P12-P18] - this worked to some degree, but turned out to be a hard problem. This is computational many-body physics at the interface of quantum information and field theory. With U. Schollwöck and A. Millis.

P18 Imaginary-time matrix product state impurity solver for dynamical mean-field theory

__FA Wolf__, A Go, IP McCulloch, AJ Millis, U Schollwöck

Physical Review X (2015) arXiv pdf

Physical Review X (2015) arXiv pdf

P17 How to discretize a quantum bath for real-time evolution

Id Vega, U Schollwöck,__FA Wolf__

Physical Review B (2015) arXiv pdf

Id Vega, U Schollwöck,

Physical Review B (2015) arXiv pdf

P16 Non-thermal melting of Neel order in the Hubbard model

K Balzer,__FA Wolf__, IP McCulloch, P Werner, M Eckstein

Physical Review X (2015) arXiv pdf

K Balzer,

Physical Review X (2015) arXiv pdf

P15 Strictly single-site DMRG algorithm with subspace expansion

C Hubig, IP McCulloch, U Schollwöck,__FA Wolf__

Physical Review B (2015) arXiv pdf

C Hubig, IP McCulloch, U Schollwöck,

Physical Review B (2015) arXiv pdf

P14 Spectral functions and time evolution from the Chebyshev recursion

__FA Wolf__, JA Justiniano, IP McCulloch, U Schollwöck

Physical Review B (2015) arXiv pdf

Physical Review B (2015) arXiv pdf

P13 Solving nonequilibrium dynamical mean-field theory using matrix product states

__FA Wolf__, IP McCulloch, U Schollwöck

Physical Review B (2014) arXiv pdf

Physical Review B (2014) arXiv pdf

P12 Chebyshev matrix product state impurity solver for dynamical mean-field theory

__FA Wolf__, IP McCulloch, O Parcollet, U Schollwöck

Physical Review B (2014) arXiv pdf

Physical Review B (2014) arXiv pdf

The low energy conversion efficiency of established solar cells is largely due to chemical imperfections of the material at which excited photons recombine. While at Bosch research, I established models for material syntheses to optimize processes for the minimization of such imperfections [O5,P8-P11]. Mathematically, these models reduce to diffusion-reaction equations. I wrote a proprietary software, which was productionized at Bosch Solar Energy. With P. Pichler.

O5 Modeling of annealing processes for ion-implanted single-crystalline silicon solar cells

__FA Wolf__

PhD Thesis (2014) pdf

PhD Thesis (2014) pdf

P11 Electrical and structural analysis of crystal defects after high-temperature rapid thermal annealing of highly boron ion-implanted emitters

J Krügener, R Peibst,__FA Wolf__, E Bugiel, T Ohrdes, F Kiefer, C Schollhorn, A Grohe, R Brendel, HJ Osten

IEEE Journal of Photovoltaics (2014) ResearchGate pdf

J Krügener, R Peibst,

IEEE Journal of Photovoltaics (2014) ResearchGate pdf

P10 Diffusion and segregation model for the annealing of silicon solar cells implanted with phosphorus

__FA Wolf__, A Martinez-Limia, D Grote, D Stichtenoth, P Pichler

IEEE Journal of Photovoltaics (2014) ResearchGate pdf

IEEE Journal of Photovoltaics (2014) ResearchGate pdf

P9 Modeling the annealing of dislocation loops in implanted c-Si solar cells

__FA Wolf__, A Martinez-Limia, D Stichtenoth, P Pichler

IEEE Journal of Photovoltaics (2014) ResearchGate pdf

IEEE Journal of Photovoltaics (2014) ResearchGate pdf

P8 A comprehensive model for the diffusion of boron in silicon in presence of fluorine

__FA Wolf__, A Martinez-Limia, P Pichler

Solid-State Electronics (2013) ResearchGate pdf

Solid-State Electronics (2013) ResearchGate pdf

The quantum Rabi model is the basic model for understanding decoherence of a Q-bit that is coupled to a bath, and hence, a basic model for the technical foundations of quantum computing [P6,P7]. By exploiting a recent exact solution of the static system, we established several dynamical properties, amonth others, Schroedinger-cat like states that show particular robustness towards decoherence. With D. Braak.

P7 Dynamical correlation functions and the quantum Rabi model

__FA Wolf__, F Vallone, G Romero, M Kollar, E Solano, D Braak

Physical Review A (2013) arXiv pdf

Physical Review A (2013) arXiv pdf

P6 Exact real-time dynamics of the quantum Rabi model

__FA Wolf__, M Kollar, D Braak

Physical Review A (2012) arXiv pdf

Physical Review A (2012) arXiv pdf

During studies, I focused on emergent properties of quantum-many body systems and their applications. Using a phenomenological theory of superconductivity (Bogoliubov de Gennes), we showed how grain boundaries and strong correlations affect high-temperature superconductivity [P5]. With T. Kopp.

O4 Supercurrent through grain boundaries in the presence of strong correlations

__FA Wolf__

Master’s Thesis (2011) pdf

Master’s Thesis (2011) pdf

P5 Supercurrent through grain boundaries in the presence of strong correlations

__FA Wolf__, S Graser, F Loder, T Kopp

Physical Review Letters (2012) arXiv pdf

Physical Review Letters (2012) arXiv pdf

Collapse and revival oscillations and coherent expansions have been suggested for realizing matter-wave lasers. The following two projects [P2,P4] provided first in-depth models in one- and two-dimensional lattices. With M. Rigol.

P4 Expansion of Bose-Hubbard Mott insulators in optical lattices

M Jreissaty, J Carrasquilla,__FA Wolf__, M Rigol

Physical Review A (2011) arXiv pdf

M Jreissaty, J Carrasquilla,

Physical Review A (2011) arXiv pdf

P2 Collapse and revival oscillations as a probe for the tunneling amplitude in an ultra-cold Bose gas

__FA Wolf__, I Hen, M Rigol

Physical Review A (2010) arXiv pdf

Physical Review A (2010) arXiv pdf

We investigated the non-equilibrium behavior of quantum many-body systems [P1-P4], in particular, the fundamental problem of how such systems transition from an excited state to equilibrium. This happens through chaotic dynamics in the classical case, but is an active area of research in the quantum case. We showed that the transition proceeds through an intermediate, prethermalized, plateau for which we developed a statistical theory. I contributed the central analytical calculation [T1] to the highly cited paper [P3] during a summer lab project. With M. Kollar.

P3 Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems

M Kollar,__FA Wolf__, M Eckstein

Physical Review B (2011) arXiv pdf

M Kollar,

Physical Review B (2011) arXiv pdf

P1 New theoretical approaches for correlated systems in nonequilibrium

M Eckstein, A Hackl, S Kehrein, M Kollar, M Moeckel, P Werner,__FA Wolf__

The European Physical Journal Special Topics (2009) arXiv pdf

M Eckstein, A Hackl, S Kehrein, M Kollar, M Moeckel, P Werner,

The European Physical Journal Special Topics (2009) arXiv pdf

During high school, I tried to gain a better understanding of how philosophical and political ideas stimulate change in society and culture. In my thesis, I investigated why J.-P. Sartre publicly supported the German terrorist group RAF upon his visit in Stammheim in 1974 [O1]. For more context, see Der Spiegel (2013).

O1 Sartre à Stammheim: son éxistentialisme et l'idéologie de la fraction armée rouge

__FA Wolf__

High School Thesis (2005) pdf

High School Thesis (2005) pdf