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We construct a reduced, data-driven, parameter dependent effective Stochastic Differential Equation (eSDE) for electric-field mediated colloidal crystallization using data obtained from Brownian Dynamics Simulations. We use Diffusion Maps (a manifold learning algorithm) to identify a set of useful latent observables. In this latent space we identify an eSDE using a deep learning architecture inspired by numerical stochastic integrators and compare it with the traditional Kramers-Moyal expansion estimation. We show that the obtained variables and the learned dynamics accurately encode the physics of the Brownian Dynamic Simulations. We further illustrate that our reduced model captures the dynamics of corresponding experimental data. Our dimension reduction/reduced model identification approach can be easily ported to a broad class of particle systems dynamics experiments/models.

In many modern statistical problems, the limited available data must be used both to develop the hypotheses to test, and to test these hypotheses-that is, both for exploratory and confirmatory data analysis. Reusing the same dataset for both exploration and testing can lead to massive selection bias, leading to many false discoveries. Selective inference is a framework that allows for performing valid inference even when the same data is reused for exploration and testing. In this work, we are interested in the problem of selective inference for data clustering, where a clustering procedure is used to hypothesize a separation of the data points into a collection of subgroups, and we then wish to test whether these data-dependent clusters in fact represent meaningful differences within the data. Recent work by Gao et al. [2022] provides a framework for doing selective inference for this setting, where the hierarchical clustering algorithm is used for producing the cluster assignments, which was then extended to k-means clustering by Chen and Witten [2022]. Both these works rely on assuming a known covariance structure for the data, but in practice, the noise level needs to be estimated-and this is particularly challenging when the true cluster structure is unknown. In our work, we extend to the setting of noise with unknown variance, and provide a selective inference method for this more general setting. Empirical results show that our new method is better able to maintain high power while controlling Type I error when the true noise level is unknown.

Earlier studies revealed that Maxwell's demon must obey the second law of thermodynamics. However, the presence of a physical principle explaining whether using information is profitable and inevitable remains uncertain. This paper reports a novel generalization of the second law of thermodynamics, answering whether such a physical principle exists in the affirmative. The entropy production can be split into two contributions: the entropy production of the individual subsystems and the reduction in the correlations between subsystems. This novel generalization of the second law implies that if an agent exploits the latter factor, then information is indispensable and provides free energy or mechanical work outweighing the operational cost. In particular, the total entropy production has a lower bound corresponding to the positive quantity that emerges when the internal correlations of the controlled target diminish, but the correlations between the agent and target do not exist. Therefore, the information about the target is indispensable for exploiting the internal correlations to extract free energy or work. Furthermore, as the internal correlations can grow linearly with the number of the subsystems constituting the target system, control with such correlations, i.e., feedback control, can yield substantial gain that exceeds the operational cost of performing feedback control, which is negligible in the thermodynamic limit. Thus, the generalized second law presented in this paper can be interpreted as a physical principle that ensures the benefit and inevitability of information processing.

Physics-based simulation of mesh based domains remains a challenging task. State-of-the-art techniques can produce realistic results but require expert knowledge. A major bottleneck in many approaches is the step of integrating a potential energy in order to compute velocities or displacements. Recently, learning based method for physics-based simulation have sparked interest with graph based approaches being a promising research direction. One of the challenges for these methods is to generate models that are mesh independent and generalize to different material properties. Moreover, the model should also be able to react to unforeseen external forces like ubiquitous collisions. Our contribution is based on a simple observation: evaluating forces is computationally relatively cheap for traditional simulation methods and can be computed in parallel in contrast to their integration. If we learn how a system reacts to forces in general, irrespective of their origin, we can learn an integrator that can predict state changes due to the total forces with high generalization power. We effectively factor out the physical model behind resulting forces by relying on an opaque force module. We demonstrate that this idea leads to a learnable module that can be trained on basic internal forces of small mesh patches and generalizes to different mesh typologies, resolutions, material parameters and unseen forces like collisions at inference time. Our proposed paradigm is general and can be used to model a variety of physical phenomena. We focus our exposition on the detail enhancement of coarse clothing geometry which has many applications including computer games, virtual reality and virtual try-on.

Much hope for finding new physics phenomena at microscopic scale relies on the observations obtained from High Energy Physics experiments, like the ones performed at the Large Hadron Collider (LHC). However, current experiments do not indicate clear signs of new physics that could guide the development of additional Beyond Standard Model (BSM) theories. Identifying signatures of new physics out of the enormous amount of data produced at the LHC falls into the class of anomaly detection and constitutes one of the greatest computational challenges. In this article, we propose a novel strategy to perform anomaly detection in a supervised learning setting, based on the artificial creation of anomalies through a random process. For the resulting supervised learning problem, we successfully apply classical and quantum Support Vector Classifiers (CSVC and QSVC respectively) to identify the artificial anomalies among the SM events. Even more promising, we find that employing an SVC trained to identify the artificial anomalies, it is possible to identify realistic BSM events with high accuracy. In parallel, we also explore the potential of quantum algorithms for improving the classification accuracy and provide plausible conditions for the best exploitation of this novel computational paradigm.

Limited look-ahead game solving for imperfect-information games is the breakthrough that allowed defeating expert humans in large poker. The existing algorithms of this type assume that all players are perfectly rational and do not allow explicit modeling and exploitation of the opponent's flaws. As a result, even very weak opponents can tie or lose only very slowly against these powerful methods. We present the first algorithm that allows incorporating opponent models into limited look-ahead game solving. Using only an approximation of a single (optimal) value function, the algorithm efficiently exploits an arbitrary estimate of the opponent's strategy. It guarantees a bounded worst-case loss for the player. We also show that using existing resolving gadgets is problematic and why we need to keep the previously solved parts of the game. Experiments on three different games show that over half of the maximum possible exploitation is achieved by our algorithm without risking almost any loss.

Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.

The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.

Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.