Steerable convolutional neural networks (CNNs) provide a general framework for building neural networks equivariant to translations and transformations of an origin-preserving group $G$, such as reflections and rotations. They rely on standard convolutions with $G$-steerable kernels obtained by analytically solving the group-specific equivariance constraint imposed onto the kernel space. As the solution is tailored to a particular group $G$, implementing a kernel basis does not generalize to other symmetry transformations, complicating the development of general group equivariant models. We propose using implicit neural representation via multi-layer perceptrons (MLPs) to parameterize $G$-steerable kernels. The resulting framework offers a simple and flexible way to implement Steerable CNNs and generalizes to any group $G$ for which a $G$-equivariant MLP can be built. We prove the effectiveness of our method on multiple tasks, including N-body simulations, point cloud classification and molecular property prediction.

We formulate a data independent latent space regularisation constraint for general unsupervised autoencoders. The regularisation rests on sampling the autoencoder Jacobian in Legendre nodes, being the centre of the Gauss-Legendre quadrature. Revisiting this classic enables to prove that regularised autoencoders ensure a one-to-one re-embedding of the initial data manifold to its latent representation. Demonstrations show that prior proposed regularisation strategies, such as contractive autoencoding, cause topological defects already for simple examples, and so do convolutional based (variational) autoencoders. In contrast, topological preservation is ensured already by standard multilayer perceptron neural networks when being regularised due to our contribution. This observation extends through the classic FashionMNIST dataset up to real world encoding problems for MRI brain scans, suggesting that, across disciplines, reliable low dimensional representations of complex high-dimensional datasets can be delivered due to this regularisation technique.

Understanding and control of Laser-driven Free Electron Lasers remain to be difficult problems that require highly intensive experimental and theoretical research. The gap between simulated and experimentally collected data might complicate studies and interpretation of obtained results. In this work we developed a deep learning based surrogate that could help to fill in this gap. We introduce a surrogate model based on normalising flows for conditional phase-space representation of electron clouds in a FEL beamline. Achieved results let us discuss further benefits and limitations in exploitability of the models to gain deeper understanding of fundamental processes within a beamline.

Modelling the temperature of Electric Vehicle (EV) batteries is a fundamental task of EV manufacturing. Extreme temperatures in the battery packs can affect their longevity and power output. Although theoretical models exist for describing heat transfer in battery packs, they are computationally expensive to simulate. Furthermore, it is difficult to acquire data measurements from within the battery cell. In this work, we propose a data-driven surrogate model (LiFe-net) that uses readily accessible driving diagnostics for battery temperature estimation to overcome these limitations. This model incorporates Neural Operators with a traditional numerical integration scheme to estimate the temperature evolution. Moreover, we propose two further variations of the baseline model: LiFe-net trained with a regulariser and LiFe-net trained with time stability loss. We compared these models in terms of generalization error on test data. The results showed that LiFe-net trained with time stability loss outperforms the other two models and can estimate the temperature evolution on unseen data with a relative error of 2.77 % on average.

While the interaction of ultra-intense ultra-short laser pulses with near- and overcritical plasmas cannot be directly observed, experimentally accessible quantities (observables) often only indirectly give information about the underlying plasma dynamics. Furthermore, the information provided by observables is incomplete, making the inverse problem highly ambiguous. Therefore, in order to infer plasma dynamics as well as experimental parameter, the full distribution over parameters given an observation needs to considered, requiring that models are flexible and account for the information lost in the forward process. Invertible Neural Networks (INNs) have been designed to efficiently model both the forward and inverse process, providing the full conditional posterior given a specific measurement. In this work, we benchmark INNs and standard statistical methods on synthetic electron spectra. First, we provide experimental results with respect to the acceptance rate, where our results show increases in acceptance rates up to a factor of 10. Additionally, we show that this increased acceptance rate also results in an increased speed-up for INNs to the same extent. Lastly, we propose a composite algorithm that utilizes INNs and promises low runtimes while preserving high accuracy.

The upcoming exascale era will provide a new generation of physics simulations. These simulations will have a high spatiotemporal resolution, which will impact the training of machine learning models since storing a high amount of simulation data on disk is nearly impossible. Therefore, we need to rethink the training of machine learning models for simulations for the upcoming exascale era. This work presents an approach that trains a neural network concurrently to a running simulation without storing data on a disk. The training pipeline accesses the training data by in-memory streaming. Furthermore, we apply methods from the domain of continual learning to enhance the generalization of the model. We tested our pipeline on the training of a 3d autoencoder trained concurrently to laser wakefield acceleration particle-in-cell simulation. Furthermore, we experimented with various continual learning methods and their effect on the generalization.

Normalizing flows are prominent deep generative models that provide tractable probability distributions and efficient density estimation. However, they are well known to fail while detecting Out-of-Distribution (OOD) inputs as they directly encode the local features of the input representations in their latent space. In this paper, we solve this overconfidence issue of normalizing flows by demonstrating that flows, if extended by an attention mechanism, can reliably detect outliers including adversarial attacks. Our approach does not require outlier data for training and we showcase the efficiency of our method for OOD detection by reporting state-of-the-art performance in diverse experimental settings.

Epilepsy is the most common neurological disorder and an accurate forecast of seizures would help to overcome the patient's uncertainty and helplessness. In this contribution, we present and discuss a novel methodology for the classification of intracranial electroencephalography (iEEG) for seizure prediction. Contrary to previous approaches, we categorically refrain from an extraction of hand-crafted features and use a convolutional neural network (CNN) topology instead for both the determination of suitable signal characteristics and the binary classification of preictal and interictal segments. Three different models have been evaluated on public datasets with long-term recordings from four dogs and three patients. Overall, our findings demonstrate the general applicability. In this work we discuss the strengths and limitations of our methodology.