Our system incorporates several key components, including a Finite Element Method (FEM)-based soft body model for simulating the sensing elastomer, a multi-material simulator for modeling diverse object types (such as elastic, elastoplastic, cables) under manipulation, a penalty-based contact model for handling contact dynamics. Additionally, we introduce a method to infer the optical response of our tactile sensor to contact using an efficient pixel-based neural module. In the goal of enabling robots to perform human-level manipulation on a diverse set of tasks, touch is one of the most prominent components. Tactile sensing, as a modality, is unique in the sense that it provides accurate, fine-detailed information about environmental interactions in the form of contact geometries and forces. Although its efficacy has been highlighted by prior research, providing crucial feedback in grasping fragile objects (Ishikawa et al., 2022), enabling robots to perform in occluded environment (Yu & Rodriguez, 2018), and detecting incipient slip (Chen et al., 2018) for highly reactive grasping, there are still advances in tactile sensing to be made especially in the form of simulation. Physics-based simulation has become a significant practical tool in the domain of robotics, by mitigating the challenges of real-world design and verification of learning algorithms. This work was done during an internship at the MIT-IBM Watson AI Lab. To accurately simulate tactile sensors which are inherently soft, it is essential to model soft body interaction's contact geometries, forces, and dynamics. Prior work (Si & Yuan, 2022) attempted to simulate contact geometries and forces for tactile sensors under (quasi-)static scenarios, and it was successfully applied to robotic perception tasks such as object shape estimation (Suresh et al., 2022), and grasp stability prediction (Si et al., 2022). However, highly dynamic manipulation tasks have not been thoroughly explored. Other prior works approach contact dynamics by either approximating sensor surface deformation using rigid-body dynamics (Xu et al., 2023) or using physics-based soft-body simulation methods such as Finite Element Method (FEM) (Narang et al., 2021). However, these methods are still limited to manipulating rigid objects.

The design of revenue-maximizing combinatorial auctions, i.e. multi-item auctions over bundles of goods, is one of the most fundamental problems in computational economics, unsolved even for two bidders and two items for sale. In the traditional economic models, it is assumed that the bidders' valuations are drawn from an underlying distribution and that the auction designer has perfect knowledge of this distribution. Despite this strong and oftentimes unrealistic assumption, it is remarkable that the revenue-maximizing combinatorial auction remains unknown. In recent years, automated mechanism design has emerged as one of the most practical and promising approaches to designing high-revenue combinatorial auctions. The most scalable automated mechanism design algorithms take as input samples from the bidders' valuation distribution and then search for a high-revenue auction in a rich auction class. In this work, we provide the first sample complexity analysis for the standard hierarchy of deterministic combinatorial auction classes used in automated mechanism design. In particular, we provide tight sample complexity bounds on the number of samples needed to guarantee that the empirical revenue of the designed mechanism on the samples is close to its expected revenue on the underlying, unknown distribution over bidder valuations, for each of the auction classes in the hierarchy. In addition to helping set automated mechanism design on firm foundations, our results also push the boundaries of learning theory. In particular, the hypothesis functions used in our contexts are defined through multi-stage combinatorial optimization procedures, rather than simple decision boundaries, as are common in machine learning.

Dexterous in-hand manipulation is an essential skill of production and life. Nevertheless, the highly stiff and mutable features of contacts cause limitations to real-time contact discovery and inference, which degrades the performance of model-based methods. Inspired by recent advancements in contact-rich locomotion and manipulation, this paper proposes a novel model-based approach to control dexterous in-hand manipulation and overcome the current limitations. The proposed approach has the attractive feature, which allows the robot to robustly execute long-horizon in-hand manipulation without pre-defined contact sequences or separated planning procedures. Specifically, we design a contact-implicit model predictive controller at high-level to generate real-time contact plans, which are executed by the low-level tracking controller. Compared with other model-based methods, such a long-horizon feature enables replanning and robust execution of contact-rich motions to achieve large-displacement in-hand tasks more efficiently; Compared with existing learning-based methods, the proposed approach achieves the dexterity and also generalizes to different objects without any pre-training. Detailed simulations and ablation studies demonstrate the efficiency and effectiveness of our method. It runs at 20Hz on the 23-degree-of-freedom long-horizon in-hand object rotation task.

In this work, we address the challenge of efficiently modeling dynamical systems in process engineering. We use reduced-order model learning, specifically operator inference. This is a non-intrusive, data-driven method for learning dynamical systems from time-domain data. The application in our study is carbon dioxide methanation, an important reaction within the Power-to-X framework, to demonstrate its potential. The numerical results show the ability of the reduced-order models constructed with operator inference to provide a reduced yet accurate surrogate solution. This represents an important milestone towards the implementation of fast and reliable digital twin architectures.

We present a novel physics-constrained polynomial chaos expansion as a surrogate modeling method capable of performing both scientific machine learning (SciML) and uncertainty quantification (UQ) tasks. The proposed method possesses a unique capability: it seamlessly integrates SciML into UQ and vice versa, which allows it to quantify the uncertainties in SciML tasks effectively and leverage SciML for improved uncertainty assessment during UQ-related tasks. The proposed surrogate model can effectively incorporate a variety of physical constraints, such as governing partial differential equations (PDEs) with associated initial and boundary conditions constraints, inequality-type constraints (e.g., monotonicity, convexity, non-negativity, among others), and additional a priori information in the training process to supplement limited data. This ensures physically realistic predictions and significantly reduces the need for expensive computational model evaluations to train the surrogate model. Furthermore, the proposed method has a built-in uncertainty quantification (UQ) feature to efficiently estimate output uncertainties. To demonstrate the effectiveness of the proposed method, we apply it to a diverse set of problems, including linear/non-linear PDEs with deterministic and stochastic parameters, data-driven surrogate modeling of a complex physical system, and UQ of a stochastic system with parameters modeled as random fields.

Current hydrological modeling methods combine data-driven Machine Learning (ML) algorithms and traditional physics-based models to address their respective limitations incorrect parameter estimates from rigid physics-based models and the neglect of physical process constraints by ML algorithms. Despite the accuracy of ML in outcome prediction, the integration of scientific knowledge is crucial for reliable predictions. This study introduces a Physics Informed Machine Learning (PIML) model, which merges the process understanding of conceptual hydrological models with the predictive efficiency of ML algorithms. Applied to the Anandapur sub-catchment, the PIML model demonstrates superior performance in forecasting monthly streamflow and actual evapotranspiration over both standalone conceptual models and ML algorithms, ensuring physical consistency of the outputs. This study replicates the methodologies of Bhasme, P., Vagadiya, J., & Bhatia, U. (2022) from their pivotal work on Physics Informed Machine Learning for hydrological processes, utilizing their shared code and datasets to further explore the predictive capabilities in hydrological modeling.

Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a partial differential equation that quantifies the physical inconsistency. We prove that for linear differential priors, the problem can be formulated as a kernel regression task. Taking advantage of kernel theory, we derive convergence rates for the minimizer of the regularized risk and show that it converges at least at the Sobolev minimax rate. However, faster rates can be achieved, depending on the physical error. This principle is illustrated with a one-dimensional example, supporting the claim that regularizing the empirical risk with physical information can be beneficial to the statistical performance of estimators.

Despite the basic premise that next-generation wireless networks (e.g., 6G) will be artificial intelligence (AI)-native, to date, most existing efforts remain either qualitative or incremental extensions to existing "AI for wireless" paradigms. Indeed, creating AI-native wireless networks faces significant technical challenges due to the limitations of data-driven, training-intensive AI. These limitations include the black-box nature of the AI models, their curve-fitting nature, which can limit their ability to reason and adapt, their reliance on large amounts of training data, and the energy inefficiency of large neural networks. In response to these limitations, this article presents a comprehensive, forward-looking vision that addresses these shortcomings by introducing a novel framework for building AI-native wireless networks; grounded in the emerging field of causal reasoning. Causal reasoning, founded on causal discovery, causal representation learning, and causal inference, can help build explainable, reasoning-aware, and sustainable wireless networks. Towards fulfilling this vision, we first highlight several wireless networking challenges that can be addressed by causal discovery and representation, including ultra-reliable beamforming for terahertz (THz) systems, near-accurate physical twin modeling for digital twins, training data augmentation, and semantic communication. We showcase how incorporating causal discovery can assist in achieving dynamic adaptability, resilience, and cognition in addressing these challenges. Furthermore, we outline potential frameworks that leverage causal inference to achieve the overarching objectives of future-generation networks, including intent management, dynamic adaptability, human-level cognition, reasoning, and the critical element of time sensitivity.

Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to provide a comprehensive review of currently available results on the numerical analysis of PINNs and related models that constitute the backbone of physics-informed machine learning. We provide a unified framework in which analysis of the various components of the error incurred by PINNs in approximating PDEs can be effectively carried out. A detailed review of available results on approximation, generalization and training errors and their behavior with respect to the type of the PDE and the dimension of the underlying domain is presented. In particular, the role of the regularity of the solutions and their stability to perturbations in the error analysis is elucidated. Numerical results are also presented to illustrate the theory. We identify training errors as a key bottleneck which can adversely affect the overall performance of various models in physics-informed machine learning.

These approaches fall into four categories: physicconstrained, Over recent decades, advances in mechanics and electronics serial, parallel, and ensemble strategies. In have led to the development of increasingly sophisticated the physic-constrained category, techniques either integrate systems with complex and multi-physics dynamics, exposing physically meaningful features from first principles into limitations in first principle-based representations [17]. ML models or explicitly include physical constraints, such Modeling these advanced systems purely based on domain as boundary conditions, into the loss function (see, e.g., knowledge may inadequately capture the overall system behavior, the working principle of physics-informed neural networks often necessitating the formulation of complex partial (PINN)) [7,?].