Physics-informed machine learning provides an approach to combining data and governing physics laws for solving complex partial differential equations (PDEs). However, efficiently solving PDEs with varying parameters and changing initial conditions and boundary conditions (ICBCs) with theoretical guarantees remains an open challenge. We propose a hybrid framework that uses a neural network to learn B-spline control points to approximate solutions to PDEs with varying system and ICBC parameters. The proposed network can be trained efficiently as one can directly specify ICBCs without imposing losses, calculate physics-informed loss functions through analytical formulas, and requires only learning the weights of B-spline functions as opposed to both weights and basis as in traditional neural operator learning methods. We provide theoretical guarantees that the proposed B-spline networks serve as universal approximators for the set of solutions of PDEs with varying ICBCs under mild conditions and establish bounds on the generalization errors in physics-informed learning. We also demonstrate in experiments that the proposed B-spline network can solve problems with discontinuous ICBCs and outperforms existing methods, and is able to learn solutions of 3D dynamics with diverse initial conditions.

Accurate estimate of long-term risk is critical for safe decision-making, but sampling from rare risk events and long-term trajectories can be prohibitively costly. Risk gradient can be used in many first-order techniques for learning and control methods, but gradient estimate is difficult to obtain using Monte Carlo (MC) methods because the infinitesimal divisor may significantly amplify sampling noise. Motivated by this gap, we propose an efficient method to evaluate long-term risk probabilities and their gradients using short-term samples without sufficient risk events. We first derive that four types of long-term risk probability are solutions of certain partial differential equations (PDEs). Then, we propose a physics-informed learning technique that integrates data and physics information (aforementioned PDEs). The physics information helps propagate information beyond available data and obtain provable generalization beyond available data, which in turn enables long-term risk to be estimated using short-term samples of safe events. Finally, we demonstrate in simulation that the proposed technique has improved sample efficiency, generalizes well to unseen regions, and adapts to changing system parameters.

This paper addresses the design of safety certificates for stochastic systems, with a focus on ensuring long-term safety through fast real-time control. In stochastic environments, set invariance-based methods that restrict the probability of risk events in infinitesimal time intervals may exhibit significant long-term risks due to cumulative uncertainties/risks. On the other hand, reachability-based approaches that account for the long-term future may require prohibitive computation in real-time decision making. To overcome this challenge involving stringent long-term safety vs. computation tradeoffs, we first introduce a novel technique termed `probabilistic invariance'. This technique characterizes the invariance conditions of the probability of interest. When the target probability is defined using long-term trajectories, this technique can be used to design myopic conditions/controllers with assured long-term safe probability. Then, we integrate this technique into safe control and learning. The proposed control methods efficiently assure long-term safety using neural networks or model predictive controllers with short outlook horizons. The proposed learning methods can be used to guarantee long-term safety during and after training. Finally, we demonstrate the performance of the proposed techniques in numerical simulations.

Accurate estimates of long-term risk probabilities and their gradients are critical for many stochastic safe control methods. However, computing such risk probabilities in real-time and in unseen or changing environments is challenging. Monte Carlo (MC) methods cannot accurately evaluate the probabilities and their gradients as an infinitesimal devisor can amplify the sampling noise. In this paper, we develop an efficient method to evaluate the probabilities of long-term risk and their gradients. The proposed method exploits the fact that long-term risk probability satisfies certain partial differential equations (PDEs), which characterize the neighboring relations between the probabilities, to integrate MC methods and physics-informed neural networks. We provide theoretical guarantees of the estimation error given certain choices of training configurations. Numerical results show the proposed method has better sample efficiency, generalizes well to unseen regions, and can adapt to systems with changing parameters. The proposed method can also accurately estimate the gradients of risk probabilities, which enables first- and second-order techniques on risk probabilities to be used for learning and control.

The quest for accurate prediction of drug molecule properties poses a fundamental challenge in the realm of Artificial Intelligence Drug Discovery (AIDD). An effective representation of drug molecules emerges as a pivotal component in this pursuit. Contemporary leading-edge research predominantly resorts to self-supervised learning (SSL) techniques to extract meaningful structural representations from large-scale, unlabeled molecular data, subsequently fine-tuning these representations for an array of downstream tasks. However, an inherent shortcoming of these studies lies in their singular reliance on one modality of molecular information, such as molecule image or SMILES representations, thus neglecting the potential complementarity of various molecular modalities. In response to this limitation, we propose MolIG, a novel MultiModaL molecular pre-training framework for predicting molecular properties based on Image and Graph structures. MolIG model innovatively leverages the coherence and correlation between molecule graph and molecule image to execute self-supervised tasks, effectively amalgamating the strengths of both molecular representation forms. This holistic approach allows for the capture of pivotal molecular structural characteristics and high-level semantic information. Upon completion of pre-training, Graph Neural Network (GNN) Encoder is used for the prediction of downstream tasks. In comparison to advanced baseline models, MolIG exhibits enhanced performance in downstream tasks pertaining to molecular property prediction within benchmark groups such as MoleculeNet Benchmark Group and ADMET Benchmark Group.

We focus on the problem of how we can enable a robot to collaborate seamlessly with a human partner, specifically in scenarios like collaborative manufacturing where prexisting data is sparse. Much prior work in human-robot collaboration uses observational models of humans (i.e. models that treat the robot purely as an observer) to choose the robot's behavior, but such models do not account for the influence the robot has on the human's actions, which may lead to inefficient interactions. We instead formulate the problem of optimally choosing a collaborative robot's behavior based on a conditional model of the human that depends on the robot's future behavior. First, we propose a novel model-based formulation of conditional behavior prediction that allows the robot to infer the human's intentions based on its future plan in data-sparse environments. We then show how to utilize a conditional model for proactive goal selection and path generation around human collaborators. Finally, we use our proposed proactive controller in a collaborative task with real users to show that it can improve users' interactions with a robot collaborator quantitatively and qualitatively.

Medication recommendation using Electronic Health Records (EHR) is challenging due to complex medical data. Current approaches extract longitudinal information from patient EHR to personalize recommendations. However, existing models often lack sufficient patient representation and overlook the importance of considering the similarity between a patient's medication records and specific medicines. Therefore, an Attention-guided Collaborative Decision Network (ACDNet) for medication recommendation is proposed in this paper. Specifically, ACDNet utilizes attention mechanism and Transformer to effectively capture patient health conditions and medication records by modeling their historical visits at both global and local levels. ACDNet also employs a collaborative decision framework, utilizing the similarity between medication records and medicine representation to facilitate the recommendation process. The experimental results on two extensive medical datasets, MIMIC-III and MIMIC-IV, clearly demonstrate that ACDNet outperforms state-of-the-art models in terms of Jaccard, PR-AUC, and F1 score, reaffirming its superiority. Moreover, the ablation experiments provide solid evidence of the effectiveness of each module in ACDNet, validating their contribution to the overall performance. Furthermore, a detailed case study reinforces the effectiveness of ACDNet in medication recommendation based on EHR data, showcasing its practical value in real-world healthcare scenarios.