Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or accurate resolution of their solutions may be intractable. Instead, recently developed methods, including those based on parameter estimation, operator subset selection, and neural networks, allow for the data-driven discovery of both ordinary and partial differential equations (PDEs), on a spectrum of interpretability. The success of these strategies is often contingent upon the correct identification of representative equations from noisy observations of state variables and, as importantly and intertwined with that, the mathematical strategies utilized to enforce those equations. Specifically, the latter has been commonly addressed via unconstrained optimization strategies. Representing the PDE as a neural network, we propose to discover the PDE by solving a constrained optimization problem and using an intermediate state representation similar to a Physics-Informed Neural Network (PINN). The objective function of this constrained optimization problem promotes matching the data, while the constraints require that the PDE is satisfied at several spatial collocation points. We present a penalty method and a widely used trust-region barrier method to solve this constrained optimization problem, and we compare these methods on numerical examples. Our results on the Burgers' and the Korteweg-De Vreis equations demonstrate that the latter constrained method outperforms the penalty method, particularly for higher noise levels or fewer collocation points. For both methods, we solve these discovered neural network PDEs with classical methods, such as finite difference methods, as opposed to PINNs-type methods relying on automatic differentiation. We briefly highlight other small, yet crucial, implementation details.

Through the generation of a dataset of accurate band gaps for perovskite materials and the use of machine learning methods, several promising halide perovskites are identified for photovoltaic applications. As we integrate solar energy into our daily lives, it has become important to find materials that efficiently convert sunlight into electricity. While silicon has dominated solar technology so far, there is also a steady turn towards materials known as perovskites due to their lower costs and simpler manufacturing processes. The challenge, however, has been to find perovskites with the right "band gap": a specific energy range that determines how efficiently a material can absorb sunlight and convert it into electricity without losing it as heat. Now, an EPFL research project led by Haiyuan Wang and Alfredo Pasquarello, with collaborators in Shanghai and in Louvain-La-Neuve, have developed a method that combines advanced computational techniques with machine-learning to search for optimal perovskite materials for photovoltaic applications.

Physical neural networks (PNNs) are emerging paradigms for neural network acceleration due to their high-bandwidth, in-propagation analogue processing. Despite the advantages of PNN for inference, training remains a challenge. The imperfect information of the physical transformation means the failure of conventional gradient-based updates from backpropagation (BP). Here, we present the asymmetrical training (AT) method, which treats the PNN structure as a grey box. AT performs training while only knowing the last layer output and neuron topological connectivity of a deep neural network structure, not requiring information about the physical control-transformation mapping. We experimentally demonstrated the AT method on deep grey-box PNNs implemented by uncalibrated photonic integrated circuits (PICs), improving the classification accuracy of Iris flower and modified MNIST hand-written digits from random guessing to near theoretical maximum. We also showcased the consistently enhanced performance of AT over BP for different datasets, including MNIST, fashion-MNIST, and Kuzushiji-MNIST. The AT method demonstrated successful training with minimal hardware overhead and reduced computational overhead, serving as a robust light-weight training alternative to fully explore the advantages of physical computation.

Balancing the exploration-exploitation trade-off is a fundamental dilemma in reinforcement learning (RL). This issue has been systemically addressed in two main approaches, namely optimism in the face of uncertainty (OFU) and Thompson sampling (TS). The methods using OFU first construct confidence sets for the environment or model parameters given the samples observed so far. After finding the reward-maximizing or optimistic parameters within the confidence set, an optimal policy with respect to the parameters is constructed and executed [1]. Various algorithms using OFU are shown to have strong theoretical guarantees in bandits [2]. On the other hand, TS is a Bayesian method in which environment or model parameters are sampled from the posterior that is updated along the process using samples and a prior, and an optimal policy with respect to the sampled parameter is constructed and executed [3].

Recent advances in diffusion models have demonstrated their strong capabilities in generating high-fidelity samples from complex distributions through an iterative refinement process. Despite the empirical success of diffusion models in motion planning and control, the model-free nature of these methods does not leverage readily available model information and limits their generalization to new scenarios beyond the training data (e.g., new robots with different dynamics). In this work, we introduce Model-Based Diffusion (MBD), an optimization approach using the diffusion process to solve trajectory optimization (TO) problems without data. The key idea is to explicitly compute the score function by leveraging the model information in TO problems, which is why we refer to our approach as model-based diffusion. Moreover, although MBD does not require external data, it can be naturally integrated with data of diverse qualities to steer the diffusion process. We also reveal that MBD has interesting connections to sampling-based optimization. Empirical evaluations show that MBD outperforms state-of-the-art reinforcement learning and sampling-based TO methods in challenging contact-rich tasks. Additionally, MBD's ability to integrate with data enhances its versatility and practical applicability, even with imperfect and infeasible data (e.g., partial-state demonstrations for high-dimensional humanoids), beyond the scope of standard diffusion models.

We discuss prototype formation in the Hopfield network. Typically, Hebbian learning with highly correlated states leads to degraded memory performance. We show this type of learning can lead to prototype formation, where unlearned states emerge as representatives of large correlated subsets of states, alleviating capacity woes. This process has similarities to prototype learning in human cognition. We provide a substantial literature review of prototype learning in associative memories, covering contributions from psychology, statistical physics, and computer science. We analyze prototype formation from a theoretical perspective and derive a stability condition for these states based on the number of examples of the prototype presented for learning, the noise in those examples, and the number of non-example states presented. The stability condition is used to construct a probability of stability for a prototype state as the factors of stability change. We also note similarities to traditional network analysis, allowing us to find a prototype capacity. We corroborate these expectations of prototype formation with experiments using a simple Hopfield network with standard Hebbian learning. We extend our experiments to a Hopfield network trained on data with multiple prototypes and find the network is capable of stabilizing multiple prototypes concurrently. We measure the basins of attraction of the multiple prototype states, finding attractor strength grows with the number of examples and the agreement of examples. We link the stability and dominance of prototype states to the energy profile of these states, particularly when comparing the profile shape to target states or other spurious states.

Push-and-slide tasks carried out by fully-actuated aerial robots can be used for inspection and simple maintenance tasks at height, such as non-destructive testing and painting. Often, an end-effector based on multiple non-actuated contact wheels is used to contact the surface. This approach entails challenges in ensuring consistent wheel contact with a surface whose exact orientation and location might be uncertain due to sensor aliasing and drift. Using a standard full-pose controller dependent on the inaccurate surface position and orientation may cause wheels to lose contact during sliding, and subsequently lead to robot tip-over. To address the tip-over issue, we present two approaches: (1) tip-over avoidance guidelines for hardware design, and (2) control for tip-over recovery and avoidance. Physical experiments with a fully-actuated aerial vehicle were executed for a push-and-slide task on a flat surface. The resulting data is used in deriving tip-over avoidance guidelines and designing a simulator that closely captures real-world conditions. We then use the simulator to test the effectiveness and robustness of the proposed approaches in risky scenarios against uncertainties.

We introduce a novel method for safe mobile robot navigation in dynamic, unknown environments, utilizing onboard sensing to impose safety constraints without the need for accurate map reconstruction. Traditional methods typically rely on detailed map information to synthesize safe stabilizing controls for mobile robots, which can be computationally demanding and less effective, particularly in dynamic operational conditions. By leveraging recent advances in distributionally robust optimization, we develop a distributionally robust control barrier function (DR-CBF) constraint that directly processes range sensor data to impose safety constraints. Coupling this with a control Lyapunov function (CLF) for path tracking, we demonstrate that our CLF-DR-CBF control synthesis method achieves safe, efficient, and robust navigation in uncertain dynamic environments. We demonstrate the effectiveness of our approach in simulated and real autonomous robot navigation experiments, marking a substantial advancement in real-time safety guarantees for mobile robots.

In autonomous driving, multi-modal perception models leveraging inputs from multiple sensors exhibit strong robustness in degraded environments. However, these models face challenges in efficiently and effectively transferring learned representations across different modalities and tasks. This paper presents NeRF-Supervised Masked Auto Encoder (NS-MAE), a self-supervised pre-training paradigm for transferable multi-modal representation learning. NS-MAE is designed to provide pre-trained model initializations for efficient and high-performance fine-tuning. Our approach uses masked multi-modal reconstruction in neural radiance fields (NeRF), training the model to reconstruct missing or corrupted input data across multiple modalities. Specifically, multi-modal embeddings are extracted from corrupted LiDAR point clouds and images, conditioned on specific view directions and locations. These embeddings are then rendered into projected multi-modal feature maps using neural rendering techniques. The original multi-modal signals serve as reconstruction targets for the rendered feature maps, facilitating self-supervised representation learning. Extensive experiments demonstrate the promising transferability of NS-MAE representations across diverse multi-modal and single-modal perception models. This transferability is evaluated on various 3D perception downstream tasks, such as 3D object detection and BEV map segmentation, using different amounts of fine-tuning labeled data. Our code will be released to support the community.

Plant health can be monitored dynamically using multispectral sensors that measure Near-Infrared reflectance (NIR). Despite this potential, obtaining and annotating high-resolution NIR images poses a significant challenge for training deep neural networks. Typically, large networks pre-trained on the RGB domain are utilized to fine-tune infrared images. This practice introduces a domain shift issue because of the differing visual traits between RGB and NIR images.As an alternative to fine-tuning, a method called low-rank adaptation (LoRA) enables more efficient training by optimizing rank-decomposition matrices while keeping the original network weights frozen. However, existing parameter-efficient adaptation strategies for remote sensing images focus on RGB images and overlook domain shift issues in the NIR domain. Therefore, this study investigates the potential benefits of using vision transformer (ViT) backbones pre-trained in the RGB domain, with low-rank adaptation for downstream tasks in the NIR domain. Extensive experiments demonstrate that employing LoRA with pre-trained ViT backbones yields the best performance for downstream tasks applied to NIR images.