In the past years, computational models have started to help map, understand, and predict the biology of single cells.

This page covers academic research; most of the industry research of recent years is unpublished. Before 2015, I developed computational approaches to predict the emergent behavior of strongly correlated quantum materials, basic models of quantum computers, and chemical reactions in solar cells.

Software for single-cell analytics and data management

Scanpy [P23] is a scalable toolkit for analyzing single-cell gene expression data. Together with anndata [P33] it has become widely used and lead to an ecosystem of tools, with >700k downloads and >600 dependent repositories. It got featured within the first cycle of Essential Open Source Software for Science by CZI among 32 projects, alongside giants such as numpy, pandas, scikit-learn, matplotlib, and others. Also see software.

P33 anndata: Annotated data
I Virshup, S Rybakov, FJ Theis, P Angerer†, FA Wolf†
bioRxiv (2021) pdf code
P23 Scanpy: large-scale single-cell gene expression data analysis
FA Wolf, P Angerer, FJ Theis
Genome Biology (2018) bioRxiv pdf code

Dynamical modeling of RNA velocity

RNA velocity has opened up new ways of studying cellular differentiation in scRNA-seq [LaManno18] by capturing gene expression change rates based on ratios of spliced and unspliced mRNA. With scVelo [P28], 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. Also see software.

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

Generative modeling of single-cell perturbation effects

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, systems and species. While the first implementation of the approach (scGen) relied on latent space vector arithmetics, we then developed 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
P31 Machine learning for perturbational single-cell omics
Y Ji, M Lotfollahi, FA Wolf, FJ Theis
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
P27 scGen predicts single-cell perturbation responses
M Lotfollahi, FA Wolf†, FJ Theis†
Nature Methods (2019) bioRxiv pdf code

Mapping the coarse-grained connectivity of complex manifolds

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
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
P19 Diffusion pseudotime robustly reconstructs branching cellular lineages
L Haghverdi, M Büttner, FA Wolf, F Buettner, FJ Theis
Nature Methods (2016) bioRxiv pdf

Interpretable knowledge-enriched latent representations of scRNA-seq

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

Reconstructing cell cycle and disease progression using deep learning

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]. See a video.

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

Deep-learning based diagnosis of lung cancer from images

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

Solving dynamical mean-field theory using tensor trains

Optimizing tensor trains (MPS, DMRG) presents a 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 simulate otherwise incomputable emergent properties of strongly correlated materials [O6,P12-P18].

O6 Solving dynamical mean-field theory using matrix product states
FA Wolf
PhD Thesis (2015) pdf
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
P17 How to discretize a quantum bath for real-time evolution
Id Vega, U Schollwöck, FA Wolf
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
P15 Strictly single-site DMRG algorithm with subspace expansion
C Hubig, IP McCulloch, U Schollwöck, FA Wolf
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
P13 Solving nonequilibrium dynamical mean-field theory using matrix product states
FA Wolf, IP McCulloch, U Schollwöck
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

Modeling diffusion-reaction chemistry of solar cells to improve conversion efficiency

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.

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

Dynamics of the quantum Rabi model

The quantum Rabi model is the basic model for understanding decoherence of a Q-bit that is coupled to a bath, and in that sense 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.

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
P6 Exact real-time dynamics of the quantum Rabi model
FA Wolf, M Kollar, D Braak
Physical Review A (2012) arXiv pdf

Supercurrent through grain boundaries

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].

O4 Supercurrent through grain boundaries in the presence of strong correlations
FA Wolf
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

Coherent expansions of quantum matter and matter wave lasers

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.

P4 Expansion of Bose-Hubbard Mott insulators in optical lattices
M Jreissaty, J Carrasquilla, FA Wolf, M Rigol
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

Relaxation of a quantum many-body system after perturbation

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.

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
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

Sartre at Stammheim

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