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In the present work, advanced spatial and temporal discretization techniques are tailored to hyperelastic physics-augmented neural networks, i.e., neural network based constitutive models which fulfill all relevant mechanical conditions of hyperelasticity by construction. The framework takes into account the structure of neural network-based constitutive models, in particular, that their derivatives are more complex compared to analytical models. The proposed framework allows for convenient mixed Hu-Washizu like finite element formulations applicable to nearly incompressible material behavior. The key feature of this work is a tailored energy-momentum scheme for time discretization, which allows for energy and momentum preserving dynamical simulations. Both the mixed formulation and the energy-momentum discretization are applied in finite element analysis. For this, a hyperelastic physics-augmented neural network model is calibrated to data generated with an analytical potential. In all finite element simulations, the proposed discretization techniques show excellent performance. All of this demonstrates that, from a formal point of view, neural networks are essentially mathematical functions. As such, they can be applied in numerical methods as straightforwardly as analytical constitutive models. Nevertheless, their special structure suggests to tailor advanced discretization methods, to arrive at compact mathematical formulations and convenient implementations.

Despite its success, Model Predictive Control (MPC) often requires intensive task-specific engineering and tuning. On the other hand, Reinforcement Learning (RL) architectures minimize this effort, but need extensive data collection and lack interpretability and safety. An open research question is how to combine the advantages of RL and MPC to exploit the best of both worlds. This paper introduces a novel modular RL architecture that bridges these two approaches. By placing a differentiable MPC in the heart of an actor-critic RL agent, the proposed system enables short-term predictions and optimization of actions based on system dynamics, while retaining the end-to-end training benefits and exploratory behavior of an RL agent. The proposed approach effectively handles two different time-horizon scales: short-term decisions managed by the actor MPC and long term ones managed by the critic network. This provides a promising direction for RL, which combines the advantages of model-based and end-to-end learning methods. We validate the approach in simulated and real-world experiments on a quadcopter platform performing different high-level tasks, and show that the proposed method can learn complex behaviours end-to-end while retaining the properties of an MPC.

Wheeled robot navigation has been widely used in urban environments, but little research has been conducted on its navigation in wild vegetation. External sensors (LiDAR, camera etc.) are often used to construct point cloud map of the surrounding environment, however, the supporting rigid ground used for travelling cannot be detected due to the occlusion of vegetation. This often causes unsafe or not smooth path during planning process. To address the drawback, we propose the PE-RRT* algorithm, which effectively combines a novel support plane estimation method and sampling algorithm to generate real-time feasible and safe path in vegetation environments. In order to accurately estimate the support plane, we combine external perception and proprioception, and use Multivariate Gaussian Processe Regression (MV-GPR) to estimate the terrain at the sampling nodes. We build a physical experimental platform and conduct experiments in different outdoor environments. Experimental results show that our method has high safety, robustness and generalization.

While deep learning techniques have become extremely popular for solving a broad range of optimization problems, methods to enforce hard constraints during optimization, particularly on deep neural networks, remain underdeveloped. Inspired by the rich literature on meshless interpolation and its extension to spectral collocation methods in scientific computing, we develop a series of approaches for enforcing hard constraints on neural fields, which we refer to as \emph{Constrained Neural Fields} (CNF). The constraints can be specified as a linear operator applied to the neural field and its derivatives. We also design specific model representations and training strategies for problems where standard models may encounter difficulties, such as conditioning of the system, memory consumption, and capacity of the network when being constrained. Our approaches are demonstrated in a wide range of real-world applications. Additionally, we develop a framework that enables highly efficient model and constraint specification, which can be readily applied to any downstream task where hard constraints need to be explicitly satisfied during optimization.

This paper studies federated learning (FL)--especially cross-silo FL--with data from people who do not trust the server or other silos. In this setting, each silo (e.g. hospital) has data from different people (e.g. patients) and must maintain the privacy of each person's data (e.g. medical record), even if the server or other silos act as adversarial eavesdroppers. This requirement motivates the study of Inter-Silo Record-Level Differential Privacy (ISRL-DP), which requires silo i's communications to satisfy record/item-level differential privacy (DP). ISRL-DP ensures that the data of each person (e.g. patient) in silo i (e.g. hospital i) cannot be leaked. ISRL-DP is different from well-studied privacy notions. Central and user-level DP assume that people trust the server/other silos. On the other end of the spectrum, local DP assumes that people do not trust anyone at all (even their own silo). Sitting between central and local DP, ISRL-DP makes the realistic assumption (in cross-silo FL) that people trust their own silo, but not the server or other silos. In this work, we provide tight (up to logarithms) upper and lower bounds for ISRL-DP FL with convex/strongly convex loss functions and homogeneous (i.i.d.) silo data. Remarkably, we show that similar bounds are attainable for smooth losses with arbitrary heterogeneous silo data distributions, via an accelerated ISRL-DP algorithm. We also provide tight upper and lower bounds for ISRL-DP federated empirical risk minimization, and use acceleration to attain the optimal bounds in fewer rounds of communication than the state-of-the-art. Finally, with a secure "shuffler" to anonymize silo messages (but without a trusted server), our algorithm attains the optimal central DP rates under more practical trust assumptions. Numerical experiments show favorable privacy-accuracy tradeoffs for our algorithm in classification and regression tasks.

Distribution-to-Distribution (D2D) point cloud registration algorithms are fast, interpretable, and perform well in unstructured environments. Unfortunately, existing strategies for predicting solution error for these methods are overly optimistic, particularly in regions containing large or extended physical objects. In this paper we introduce the Iterative Closest Ellipsoidal Transform (ICET), a novel 3D LIDAR scan-matching algorithm that re-envisions NDT in order to provide robust accuracy prediction from first principles. Like NDT, ICET subdivides a LIDAR scan into voxels in order to analyze complex scenes by considering many smaller local point distributions, however, ICET assesses the voxel distribution to distinguish random noise from deterministic structure. ICET then uses a weighted least-squares formulation to incorporate this noise/structure distinction into computing a localization solution and predicting the solution-error covariance. In order to demonstrate the reasonableness of our accuracy predictions, we verify 3D ICET in three LIDAR tests involving real-world automotive data, high-fidelity simulated trajectories, and simulated corner-case scenes. For each test, ICET consistently performs scan matching with sub-centimeter accuracy. This level of accuracy, combined with the fact that the algorithm is fully interpretable, make it well suited for safety-critical transportation applications. Code is available at //github.com/mcdermatt/ICET

We consider the problem of estimating a scalar target parameter in the presence of nuisance parameters. Replacing the unknown nuisance parameter with a nonparametric estimator, e.g.,a machine learning (ML) model, is convenient but has shown to be inefficient due to large biases. Modern methods, such as the targeted minimum loss-based estimation (TMLE) and double machine learning (DML), achieve optimal performance under flexible assumptions by harnessing ML estimates while mitigating the plug-in bias. To avoid a sub-optimal bias-variance trade-off, these methods perform a debiasing step of the plug-in pre-estimate. Existing debiasing methods require the influence function of the target parameter as input. However, deriving the IF requires specialized expertise and thus obstructs the adaptation of these methods by practitioners. We propose a novel way to debias plug-in estimators which (i) is efficient, (ii) does not require the IF to be implemented, (iii) is computationally tractable, and therefore can be readily adapted to new estimation problems and automated without analytic derivations by the user. We build on the TMLE framework and update a plug-in estimate with a regularized likelihood maximization step over a nonparametric model constructed with a reproducing kernel Hilbert space (RKHS), producing an efficient plug-in estimate for any regular target parameter. Our method, thus, offers the efficiency of competing debiasing techniques without sacrificing the utility of the plug-in approach.

Deep reinforcement learning algorithms typically act on the same set of actions. However, this is not sufficient for a wide range of real-world applications where different subsets are available at each step. In this thesis, we consider the problem of interval restrictions as they occur in pathfinding with dynamic obstacles. When actions that lead to collisions are avoided, the continuous action space is split into variable parts. Recent research learns with strong assumptions on the number of intervals, is limited to convex subsets, and the available actions are learned from the observations. Therefore, we propose two approaches that are independent of the state of the environment by extending parameterized reinforcement learning and ConstraintNet to handle an arbitrary number of intervals. We demonstrate their performance in an obstacle avoidance task and compare the methods to penalties, projection, replacement, as well as discrete and continuous masking from the literature. The results suggest that discrete masking of action-values is the only effective method when constraints did not emerge during training. When restrictions are learned, the decision between projection, masking, and our ConstraintNet modification seems to depend on the task at hand. We compare the results with varying complexity and give directions for future work.

Graph neural networks (GNNs) is widely used to learn a powerful representation of graph-structured data. Recent work demonstrates that transferring knowledge from self-supervised tasks to downstream tasks could further improve graph representation. However, there is an inherent gap between self-supervised tasks and downstream tasks in terms of optimization objective and training data. Conventional pre-training methods may be not effective enough on knowledge transfer since they do not make any adaptation for downstream tasks. To solve such problems, we propose a new transfer learning paradigm on GNNs which could effectively leverage self-supervised tasks as auxiliary tasks to help the target task. Our methods would adaptively select and combine different auxiliary tasks with the target task in the fine-tuning stage. We design an adaptive auxiliary loss weighting model to learn the weights of auxiliary tasks by quantifying the consistency between auxiliary tasks and the target task. In addition, we learn the weighting model through meta-learning. Our methods can be applied to various transfer learning approaches, it performs well not only in multi-task learning but also in pre-training and fine-tuning. Comprehensive experiments on multiple downstream tasks demonstrate that the proposed methods can effectively combine auxiliary tasks with the target task and significantly improve the performance compared to state-of-the-art methods.

As data are increasingly being stored in different silos and societies becoming more aware of data privacy issues, the traditional centralized training of artificial intelligence (AI) models is facing efficiency and privacy challenges. Recently, federated learning (FL) has emerged as an alternative solution and continue to thrive in this new reality. Existing FL protocol design has been shown to be vulnerable to adversaries within or outside of the system, compromising data privacy and system robustness. Besides training powerful global models, it is of paramount importance to design FL systems that have privacy guarantees and are resistant to different types of adversaries. In this paper, we conduct the first comprehensive survey on this topic. Through a concise introduction to the concept of FL, and a unique taxonomy covering: 1) threat models; 2) poisoning attacks and defenses against robustness; 3) inference attacks and defenses against privacy, we provide an accessible review of this important topic. We highlight the intuitions, key techniques as well as fundamental assumptions adopted by various attacks and defenses. Finally, we discuss promising future research directions towards robust and privacy-preserving federated learning.