@article{13996, abstract = {We report the observation of an anomalous nonlinear optical response of the prototypical three-dimensional topological insulator bismuth selenide through the process of high-order harmonic generation. We find that the generation efficiency increases as the laser polarization is changed from linear to elliptical, and it becomes maximum for circular polarization. With the aid of a microscopic theory and a detailed analysis of the measured spectra, we reveal that such anomalous enhancement encodes the characteristic topology of the band structure that originates from the interplay of strong spin–orbit coupling and time-reversal symmetry protection. The implications are in ultrafast probing of topological phase transitions, light-field driven dissipationless electronics, and quantum computation.}, author = {Baykusheva, Denitsa Rangelova and Chacón, Alexis and Lu, Jian and Bailey, Trevor P. and Sobota, Jonathan A. and Soifer, Hadas and Kirchmann, Patrick S. and Rotundu, Costel and Uher, Ctirad and Heinz, Tony F. and Reis, David A. and Ghimire, Shambhu}, issn = {1530-6992}, journal = {Nano Letters}, keywords = {Mechanical Engineering, Condensed Matter Physics, General Materials Science, General Chemistry, Bioengineering}, number = {21}, pages = {8970--8978}, publisher = {American Chemical Society}, title = {{All-optical probe of three-dimensional topological insulators based on high-harmonic generation by circularly polarized laser fields}}, doi = {10.1021/acs.nanolett.1c02145}, volume = {21}, year = {2021}, } @article{13997, abstract = {We investigate theoretically the strong-field regime of light-matter interactions in the topological-insulator class of quantum materials. In particular, we focus on the process of nonperturbative high-order harmonic generation from the paradigmatic three-dimensional topological insulator bismuth selenide (Bi2Se3) subjected to intense midinfrared laser fields. We analyze the contributions from the spin-orbit-coupled bulk states and the topological surface bands separately and reveal a major difference in how their harmonic yields depend on the ellipticity of the laser field. Bulk harmonics show a monotonic decrease in their yield as the ellipticity increases, in a manner reminiscent of high harmonic generation in gaseous media. However, the surface contribution exhibits a highly nontrivial dependence, culminating with a maximum for circularly polarized fields. We attribute the observed anomalous behavior to (i) the enhanced amplitude and the circular pattern of the interband dipole and the Berry connections in the vicinity of the Dirac point and (ii) the influence of the higher-order, hexagonal warping terms in the Hamiltonian, which are responsible for the hexagonal deformation of the energy surface at higher momenta. The latter are associated directly with spin-orbit-coupling parameters. Our results thus establish the sensitivity of strong-field-driven high harmonic emission to the topology of the band structure as well as to the manifestations of spin-orbit interaction.}, author = {Baykusheva, Denitsa Rangelova and Chacón, Alexis and Kim, Dasol and Kim, Dong Eon and Reis, David A. and Ghimire, Shambhu}, issn = {2469-9934}, journal = {Physical Review A}, number = {2}, publisher = {American Physical Society}, title = {{Strong-field physics in three-dimensional topological insulators}}, doi = {10.1103/physreva.103.023101}, volume = {103}, year = {2021}, } @unpublished{14097, abstract = {UVEX is a proposed medium class Explorer mission designed to provide crucial missing capabilities that will address objectives central to a broad range of modern astrophysics. The UVEX design has two co-aligned wide-field imagers operating in the FUV and NUV and a powerful broadband medium resolution spectrometer. In its two-year baseline mission, UVEX will perform a multi-cadence synoptic all-sky survey 50/100 times deeper than GALEX in the NUV/FUV, cadenced surveys of the Large and Small Magellanic Clouds, rapid target of opportunity followup, as well as spectroscopic followup of samples of stars and galaxies. The science program is built around three pillars. First, UVEX will explore the low-mass, low-metallicity galaxy frontier through imaging and spectroscopic surveys that will probe key aspects of the evolution of galaxies by understanding how star formation and stellar evolution at low metallicities affect the growth and evolution of low-metallicity, low-mass galaxies in the local universe. Such galaxies contain half the mass in the local universe, and are analogs for the first galaxies, but observed at distances that make them accessible to detailed study. Second, UVEX will explore the dynamic universe through time-domain surveys and prompt spectroscopic followup capability will probe the environments, energetics, and emission processes in the early aftermaths of gravitational wave-discovered compact object mergers, discover hot, fast UV transients, and diagnose the early stages of stellar explosions. Finally, UVEX will become a key community resource by leaving a large all-sky legacy data set, enabling a wide range of scientific studies and filling a gap in the new generation of wide-field, sensitive optical and infrared surveys provided by the Rubin, Euclid, and Roman observatories. This paper discusses the scientific potential of UVEX, and the broad scientific program.}, author = {Kulkarni, S. R. and Harrison, Fiona A. and Grefenstette, Brian W. and Earnshaw, Hannah P. and Andreoni, Igor and Berg, Danielle A. and Bloom, Joshua S. and Cenko, S. Bradley and Chornock, Ryan and Christiansen, Jessie L. and Coughlin, Michael W. and Criswell, Alexander Wuollet and Darvish, Behnam and Das, Kaustav K. and De, Kishalay and Dessart, Luc and Dixon, Don and Dorsman, Bas and Kareem El-Badry, Kareem El-Badry and Evans, Christopher and Ford, K. E. Saavik and Fremling, Christoffer and Gansicke, Boris T. and Gezari, Suvi and Götberg, Ylva Louise Linsdotter and Green, Gregory M. and Graham, Matthew J. and Heida, Marianne and Ho, Anna Y. Q. and Jaodand, Amruta D. and Christopher M. Johns-Krull, Christopher M. Johns-Krull and Kasliwal, Mansi M. and Lazzarini, Margaret and Lu, Wenbin and Margutti, Raffaella and Martin, D. Christopher and Masters, Daniel Charles and McKernan, Barry and Naze, Yael and Nissanke, Samaya M. and Parazin, B. and Perley, Daniel A. and Phinney, E. Sterl and Piro, Anthony L. and Raaijmakers, G. and Rauw, Gregor and Rodriguez, Antonio C. and Sana, Hugues and Senchyna, Peter and Singer, Leo P. and Spake, Jessica J. and Stassun, Keivan G. and Stern, Daniel and Teplitz, Harry I. and Weisz, Daniel R. and Yao, Yuhan}, booktitle = {arXiv}, title = {{Science with the ultraviolet explorer (UVEX)}}, doi = {10.48550/arXiv.2111.15608}, year = {2021}, } @article{14117, abstract = {The two fields of machine learning and graphical causality arose and are developed separately. However, there is, now, cross-pollination and increasing interest in both fields to benefit from the advances of the other. In this article, we review fundamental concepts of causal inference and relate them to crucial open problems of machine learning, including transfer and generalization, thereby assaying how causality can contribute to modern machine learning research. This also applies in the opposite direction: we note that most work in causality starts from the premise that the causal variables are given. A central problem for AI and causality is, thus, causal representation learning, that is, the discovery of high-level causal variables from low-level observations. Finally, we delineate some implications of causality for machine learning and propose key research areas at the intersection of both communities.}, author = {Scholkopf, Bernhard and Locatello, Francesco and Bauer, Stefan and Ke, Nan Rosemary and Kalchbrenner, Nal and Goyal, Anirudh and Bengio, Yoshua}, issn = {1558-2256}, journal = {Proceedings of the IEEE}, keywords = {Electrical and Electronic Engineering}, number = {5}, pages = {612--634}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Toward causal representation learning}}, doi = {10.1109/jproc.2021.3058954}, volume = {109}, year = {2021}, } @inproceedings{14176, abstract = {Intensive care units (ICU) are increasingly looking towards machine learning for methods to provide online monitoring of critically ill patients. In machine learning, online monitoring is often formulated as a supervised learning problem. Recently, contrastive learning approaches have demonstrated promising improvements over competitive supervised benchmarks. These methods rely on well-understood data augmentation techniques developed for image data which do not apply to online monitoring. In this work, we overcome this limitation by supplementing time-series data augmentation techniques with a novel contrastive learning objective which we call neighborhood contrastive learning (NCL). Our objective explicitly groups together contiguous time segments from each patient while maintaining state-specific information. Our experiments demonstrate a marked improvement over existing work applying contrastive methods to medical time-series.}, author = {Yèche, Hugo and Dresdner, Gideon and Locatello, Francesco and Hüser, Matthias and Rätsch, Gunnar}, booktitle = {Proceedings of 38th International Conference on Machine Learning}, location = {Virtual}, pages = {11964--11974}, publisher = {ML Research Press}, title = {{Neighborhood contrastive learning applied to online patient monitoring}}, volume = {139}, year = {2021}, } @inproceedings{14177, abstract = {The focus of disentanglement approaches has been on identifying independent factors of variation in data. However, the causal variables underlying real-world observations are often not statistically independent. In this work, we bridge the gap to real-world scenarios by analyzing the behavior of the most prominent disentanglement approaches on correlated data in a large-scale empirical study (including 4260 models). We show and quantify that systematically induced correlations in the dataset are being learned and reflected in the latent representations, which has implications for downstream applications of disentanglement such as fairness. We also demonstrate how to resolve these latent correlations, either using weak supervision during training or by post-hoc correcting a pre-trained model with a small number of labels.}, author = {Träuble, Frederik and Creager, Elliot and Kilbertus, Niki and Locatello, Francesco and Dittadi, Andrea and Goyal, Anirudh and Schölkopf, Bernhard and Bauer, Stefan}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, location = {Virtual}, pages = {10401--10412}, publisher = {ML Research Press}, title = {{On disentangled representations learned from correlated data}}, volume = {139}, year = {2021}, } @inproceedings{14178, abstract = {Learning meaningful representations that disentangle the underlying structure of the data generating process is considered to be of key importance in machine learning. While disentangled representations were found to be useful for diverse tasks such as abstract reasoning and fair classification, their scalability and real-world impact remain questionable. We introduce a new high-resolution dataset with 1M simulated images and over 1,800 annotated real-world images of the same setup. In contrast to previous work, this new dataset exhibits correlations, a complex underlying structure, and allows to evaluate transfer to unseen simulated and real-world settings where the encoder i) remains in distribution or ii) is out of distribution. We propose new architectures in order to scale disentangled representation learning to realistic high-resolution settings and conduct a large-scale empirical study of disentangled representations on this dataset. We observe that disentanglement is a good predictor for out-of-distribution (OOD) task performance.}, author = {Dittadi, Andrea and Träuble, Frederik and Locatello, Francesco and Wüthrich, Manuel and Agrawal, Vaibhav and Winther, Ole and Bauer, Stefan and Schölkopf, Bernhard}, booktitle = {The Ninth International Conference on Learning Representations}, location = {Virtual}, title = {{On the transfer of disentangled representations in realistic settings}}, year = {2021}, } @inproceedings{14179, abstract = {Self-supervised representation learning has shown remarkable success in a number of domains. A common practice is to perform data augmentation via hand-crafted transformations intended to leave the semantics of the data invariant. We seek to understand the empirical success of this approach from a theoretical perspective. We formulate the augmentation process as a latent variable model by postulating a partition of the latent representation into a content component, which is assumed invariant to augmentation, and a style component, which is allowed to change. Unlike prior work on disentanglement and independent component analysis, we allow for both nontrivial statistical and causal dependencies in the latent space. We study the identifiability of the latent representation based on pairs of views of the observations and prove sufficient conditions that allow us to identify the invariant content partition up to an invertible mapping in both generative and discriminative settings. We find numerical simulations with dependent latent variables are consistent with our theory. Lastly, we introduce Causal3DIdent, a dataset of high-dimensional, visually complex images with rich causal dependencies, which we use to study the effect of data augmentations performed in practice.}, author = {Kügelgen, Julius von and Sharma, Yash and Gresele, Luigi and Brendel, Wieland and Schölkopf, Bernhard and Besserve, Michel and Locatello, Francesco}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713845393}, location = {Virtual}, pages = {16451--16467}, title = {{Self-supervised learning with data augmentations provably isolates content from style}}, volume = {34}, year = {2021}, } @inproceedings{14180, abstract = {Modern neural network architectures can leverage large amounts of data to generalize well within the training distribution. However, they are less capable of systematic generalization to data drawn from unseen but related distributions, a feat that is hypothesized to require compositional reasoning and reuse of knowledge. In this work, we present Neural Interpreters, an architecture that factorizes inference in a self-attention network as a system of modules, which we call \emph{functions}. Inputs to the model are routed through a sequence of functions in a way that is end-to-end learned. The proposed architecture can flexibly compose computation along width and depth, and lends itself well to capacity extension after training. To demonstrate the versatility of Neural Interpreters, we evaluate it in two distinct settings: image classification and visual abstract reasoning on Raven Progressive Matrices. In the former, we show that Neural Interpreters perform on par with the vision transformer using fewer parameters, while being transferrable to a new task in a sample efficient manner. In the latter, we find that Neural Interpreters are competitive with respect to the state-of-the-art in terms of systematic generalization. }, author = {Rahaman, Nasim and Gondal, Muhammad Waleed and Joshi, Shruti and Gehler, Peter and Bengio, Yoshua and Locatello, Francesco and Schölkopf, Bernhard}, booktitle = {Advances in Neural Information Processing Systems}, isbn = {9781713845393}, location = {Virtual}, pages = {10985--10998}, title = {{Dynamic inference with neural interpreters}}, volume = {34}, year = {2021}, } @inproceedings{14181, abstract = {Variational Inference makes a trade-off between the capacity of the variational family and the tractability of finding an approximate posterior distribution. Instead, Boosting Variational Inference allows practitioners to obtain increasingly good posterior approximations by spending more compute. The main obstacle to widespread adoption of Boosting Variational Inference is the amount of resources necessary to improve over a strong Variational Inference baseline. In our work, we trace this limitation back to the global curvature of the KL-divergence. We characterize how the global curvature impacts time and memory consumption, address the problem with the notion of local curvature, and provide a novel approximate backtracking algorithm for estimating local curvature. We give new theoretical convergence rates for our algorithms and provide experimental validation on synthetic and real-world datasets.}, author = {Dresdner, Gideon and Shekhar, Saurav and Pedregosa, Fabian and Locatello, Francesco and Rätsch, Gunnar}, booktitle = {Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence}, location = {Montreal, Canada}, pages = {2337--2343}, publisher = {International Joint Conferences on Artificial Intelligence}, title = {{Boosting variational inference with locally adaptive step-sizes}}, doi = {10.24963/ijcai.2021/322}, year = {2021}, } @inproceedings{14182, abstract = {When machine learning systems meet real world applications, accuracy is only one of several requirements. In this paper, we assay a complementary perspective originating from the increasing availability of pre-trained and regularly improving state-of-the-art models. While new improved models develop at a fast pace, downstream tasks vary more slowly or stay constant. Assume that we have a large unlabelled data set for which we want to maintain accurate predictions. Whenever a new and presumably better ML models becomes available, we encounter two problems: (i) given a limited budget, which data points should be re-evaluated using the new model?; and (ii) if the new predictions differ from the current ones, should we update? Problem (i) is about compute cost, which matters for very large data sets and models. Problem (ii) is about maintaining consistency of the predictions, which can be highly relevant for downstream applications; our demand is to avoid negative flips, i.e., changing correct to incorrect predictions. In this paper, we formalize the Prediction Update Problem and present an efficient probabilistic approach as answer to the above questions. In extensive experiments on standard classification benchmark data sets, we show that our method outperforms alternative strategies along key metrics for backward-compatible prediction updates.}, author = {Träuble, Frederik and Kügelgen, Julius von and Kleindessner, Matthäus and Locatello, Francesco and Schölkopf, Bernhard and Gehler, Peter}, booktitle = {35th Conference on Neural Information Processing Systems}, isbn = {9781713845393}, location = {Virtual}, pages = {116--128}, title = {{Backward-compatible prediction updates: A probabilistic approach}}, volume = {34}, year = {2021}, } @unpublished{14221, abstract = {The world is structured in countless ways. It may be prudent to enforce corresponding structural properties to a learning algorithm's solution, such as incorporating prior beliefs, natural constraints, or causal structures. Doing so may translate to faster, more accurate, and more flexible models, which may directly relate to real-world impact. In this dissertation, we consider two different research areas that concern structuring a learning algorithm's solution: when the structure is known and when it has to be discovered.}, author = {Locatello, Francesco}, booktitle = {arXiv}, title = {{Enforcing and discovering structure in machine learning}}, doi = {10.48550/arXiv.2111.13693}, year = {2021}, } @unpublished{14278, abstract = {The Birkhoff conjecture says that the boundary of a strictly convex integrable billiard table is necessarily an ellipse. In this article, we consider a stronger notion of integrability, namely, integrability close to the boundary, and prove a local version of this conjecture: a small perturbation of almost every ellipse that preserves integrability near the boundary, is itself an ellipse. We apply this result to study local spectral rigidity of ellipses using the connection between the wave trace of the Laplacian and the dynamics near the boundary and establish rigidity for almost all of them.}, author = {Koval, Illya}, booktitle = {arXiv}, title = {{Local strong Birkhoff conjecture and local spectral rigidity of almost every ellipse}}, doi = {10.48550/ARXIV.2111.12171}, year = {2021}, } @inproceedings{14332, abstract = {Learning data representations that are useful for various downstream tasks is a cornerstone of artificial intelligence. While existing methods are typically evaluated on downstream tasks such as classification or generative image quality, we propose to assess representations through their usefulness in downstream control tasks, such as reaching or pushing objects. By training over 10,000 reinforcement learning policies, we extensively evaluate to what extent different representation properties affect out-of-distribution (OOD) generalization. Finally, we demonstrate zero-shot transfer of these policies from simulation to the real world, without any domain randomization or fine-tuning. This paper aims to establish the first systematic characterization of the usefulness of learned representations for real-world OOD downstream tasks.}, author = {Träuble, Frederik and Dittadi, Andrea and Wuthrich, Manuel and Widmaier, Felix and Gehler, Peter Vincent and Winther, Ole and Locatello, Francesco and Bachem, Olivier and Schölkopf, Bernhard and Bauer, Stefan}, booktitle = {ICML 2021 Workshop on Unsupervised Reinforcement Learning}, location = {Virtual}, title = {{Representation learning for out-of-distribution generalization in reinforcement learning}}, year = {2021}, } @article{10000, abstract = {Inhibition or targeted deletion of histone deacetylase 3 (HDAC3) is neuroprotective in a variety neurodegenerative conditions, including retinal ganglion cells (RGCs) after acute optic nerve damage. Consistent with this, induced HDAC3 expression in cultured cells shows selective toxicity to neurons. Despite an established role for HDAC3 in neuronal pathology, little is known regarding the mechanism of this pathology.}, author = {Schmitt, Heather M. and Fehrman, Rachel L. and Maes, Margaret E and Yang, Huan and Guo, Lian Wang and Schlamp, Cassandra L. and Pelzel, Heather R. and Nickells, Robert W.}, issn = {1552-5783}, journal = {Investigative Ophthalmology and Visual Science}, number = {10}, publisher = {Association for Research in Vision and Ophthalmology}, title = {{Increased susceptibility and intrinsic apoptotic signaling in neurons by induced HDAC3 expression}}, doi = {10.1167/IOVS.62.10.14}, volume = {62}, year = {2021}, } @inproceedings{10002, abstract = {We present a faster symbolic algorithm for the following central problem in probabilistic verification: Compute the maximal end-component (MEC) decomposition of Markov decision processes (MDPs). This problem generalizes the SCC decomposition problem of graphs and closed recurrent sets of Markov chains. The model of symbolic algorithms is widely used in formal verification and model-checking, where access to the input model is restricted to only symbolic operations (e.g., basic set operations and computation of one-step neighborhood). For an input MDP with n vertices and m edges, the classical symbolic algorithm from the 1990s for the MEC decomposition requires O(n2) symbolic operations and O(1) symbolic space. The only other symbolic algorithm for the MEC decomposition requires O(nm−−√) symbolic operations and O(m−−√) symbolic space. A main open question is whether the worst-case O(n2) bound for symbolic operations can be beaten. We present a symbolic algorithm that requires O˜(n1.5) symbolic operations and O˜(n−−√) symbolic space. Moreover, the parametrization of our algorithm provides a trade-off between symbolic operations and symbolic space: for all 0<ϵ≤1/2 the symbolic algorithm requires O˜(n2−ϵ) symbolic operations and O˜(nϵ) symbolic space ( O˜ hides poly-logarithmic factors). Using our techniques we present faster algorithms for computing the almost-sure winning regions of ω -regular objectives for MDPs. We consider the canonical parity objectives for ω -regular objectives, and for parity objectives with d -priorities we present an algorithm that computes the almost-sure winning region with O˜(n2−ϵ) symbolic operations and O˜(nϵ) symbolic space, for all 0<ϵ≤1/2 .}, author = {Chatterjee, Krishnendu and Dvorak, Wolfgang and Henzinger, Monika H and Svozil, Alexander}, booktitle = {Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science}, isbn = {978-1-6654-4896-3}, issn = {1043-6871}, keywords = {Computer science, Computational modeling, Markov processes, Probabilistic logic, Formal verification, Game Theory}, location = {Rome, Italy}, pages = {1--13}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Symbolic time and space tradeoffs for probabilistic verification}}, doi = {10.1109/LICS52264.2021.9470739}, year = {2021}, } @inproceedings{10004, abstract = {Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization criterion is the maximal expected total reward where the MDP stops after T steps, which can be computed by a simple dynamic programming algorithm. We consider a natural generalization of the problem where the stopping times can be chosen according to a probability distribution, such that the expected stopping time is T, to optimize the expected total reward. Quite surprisingly we establish inter-reducibility of the expected stopping-time problem for Markov chains with the Positivity problem (which is related to the well-known Skolem problem), for which establishing either decidability or undecidability would be a major breakthrough. Given the hardness of the exact problem, we consider the approximate version of the problem: we show that it can be solved in exponential time for Markov chains and in exponential space for MDPs.}, author = {Chatterjee, Krishnendu and Doyen, Laurent}, booktitle = {Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science}, isbn = {978-1-6654-4896-3}, issn = {1043-6871}, keywords = {Computer science, Heuristic algorithms, Memory management, Automata, Markov processes, Probability distribution, Complexity theory}, location = {Rome, Italy}, pages = {1--13}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Stochastic processes with expected stopping time}}, doi = {10.1109/LICS52264.2021.9470595}, year = {2021}, } @article{10005, abstract = {We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first-order divergence operator acting on a flux function, which is related to the spatial gradient of the unknown through an additional implicit equation. This setting, broad enough in terms of applications, significantly expands the paradigm of nonlinear parabolic problems. Formulating four conditions concerning the form of the implicit equation, we first show that these conditions describe a maximal monotone p-coercive graph. We then establish the global-in-time and large-data existence of a (weak) solution and its uniqueness. To this end, we adopt and significantly generalize Minty’s method of monotone mappings. A unified theory, containing several novel tools, is developed in a way to be tractable from the point of view of numerical approximations.}, author = {Bulíček, Miroslav and Maringová, Erika and Málek, Josef}, issn = {1793-6314}, journal = {Mathematical Models and Methods in Applied Sciences}, keywords = {Nonlinear parabolic systems, implicit constitutive theory, weak solutions, existence, uniqueness}, number = {09}, publisher = {World Scientific}, title = {{On nonlinear problems of parabolic type with implicit constitutive equations involving flux}}, doi = {10.1142/S0218202521500457}, volume = {31}, year = {2021}, } @phdthesis{10007, abstract = {The present thesis is concerned with the derivation of weak-strong uniqueness principles for curvature driven interface evolution problems not satisfying a comparison principle. The specific examples being treated are two-phase Navier-Stokes flow with surface tension, modeling the evolution of two incompressible, viscous and immiscible fluids separated by a sharp interface, and multiphase mean curvature flow, which serves as an idealized model for the motion of grain boundaries in an annealing polycrystalline material. Our main results - obtained in joint works with Julian Fischer, Tim Laux and Theresa M. Simon - state that prior to the formation of geometric singularities due to topology changes, the weak solution concept of Abels (Interfaces Free Bound. 9, 2007) to two-phase Navier-Stokes flow with surface tension and the weak solution concept of Laux and Otto (Calc. Var. Partial Differential Equations 55, 2016) to multiphase mean curvature flow (for networks in R^2 or double bubbles in R^3) represents the unique solution to these interface evolution problems within the class of classical solutions, respectively. To the best of the author's knowledge, for interface evolution problems not admitting a geometric comparison principle the derivation of a weak-strong uniqueness principle represented an open problem, so that the works contained in the present thesis constitute the first positive results in this direction. The key ingredient of our approach consists of the introduction of a novel concept of relative entropies for a class of curvature driven interface evolution problems, for which the associated energy contains an interfacial contribution being proportional to the surface area of the evolving (network of) interface(s). The interfacial part of the relative entropy gives sufficient control on the interface error between a weak and a classical solution, and its time evolution can be computed, at least in principle, for any energy dissipating weak solution concept. A resulting stability estimate for the relative entropy essentially entails the above mentioned weak-strong uniqueness principles. The present thesis contains a detailed introduction to our relative entropy approach, which in particular highlights potential applications to other problems in curvature driven interface evolution not treated in this thesis.}, author = {Hensel, Sebastian}, issn = {2663-337X}, pages = {300}, publisher = {Institute of Science and Technology Austria}, title = {{Curvature driven interface evolution: Uniqueness properties of weak solution concepts}}, doi = {10.15479/at:ista:10007}, year = {2021}, } @unpublished{10011, abstract = {We propose a new weak solution concept for (two-phase) mean curvature flow which enjoys both (unconditional) existence and (weak-strong) uniqueness properties. These solutions are evolving varifolds, just as in Brakke's formulation, but are coupled to the phase volumes by a simple transport equation. First, we show that, in the exact same setup as in Ilmanen's proof [J. Differential Geom. 38, 417-461, (1993)], any limit point of solutions to the Allen-Cahn equation is a varifold solution in our sense. Second, we prove that any calibrated flow in the sense of Fischer et al. [arXiv:2003.05478] - and hence any classical solution to mean curvature flow - is unique in the class of our new varifold solutions. This is in sharp contrast to the case of Brakke flows, which a priori may disappear at any given time and are therefore fatally non-unique. Finally, we propose an extension of the solution concept to the multi-phase case which is at least guaranteed to satisfy a weak-strong uniqueness principle.}, author = {Hensel, Sebastian and Laux, Tim}, booktitle = {arXiv}, keywords = {Mean curvature flow, gradient flows, varifolds, weak solutions, weak-strong uniqueness, calibrated geometry, gradient-flow calibrations}, title = {{A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness}}, doi = {10.48550/arXiv.2109.04233}, year = {2021}, }