Scene representations using 3D Gaussian primitives have produced excellent results in modeling the appearance of static and dynamic 3D scenes. Many graphics applications, however, demand the ability to manipulate both the appearance and the physical properties of objects. We introduce Feature Splatting, an approach that unifies physics-based dynamic scene synthesis with rich semantics from vision language foundation models that are grounded by natural language. Our first contribution is a way to distill high-quality, object-centric vision-language features into 3D Gaussians, that enables semi-automatic scene decomposition using text queries. Our second contribution is a way to synthesize physics-based dynamics from an otherwise static scene using a particle-based simulator, in which material properties are assigned automatically via text queries. We ablate key techniques used in this pipeline, to illustrate the challenge and opportunities in using feature-carrying 3D Gaussians as a unified format for appearance, geometry, material properties and semantics grounded on natural language. Project website: https://feature-splatting.github.io/

Safe and efficient object manipulation is a key enabler of many real-world robot applications. However, this is challenging because robot operation must be robust to a range of sensor and actuator uncertainties. In this paper, we present a physics-informed causal-inference-based framework for a robot to probabilistically reason about candidate actions in a block stacking task in a partially observable setting. We integrate a physics-based simulation of the rigid-body system dynamics with a causal Bayesian network (CBN) formulation to define a causal generative probabilistic model of the robot decision-making process. Using simulation-based Monte Carlo experiments, we demonstrate our framework's ability to successfully: (1) predict block tower stability with high accuracy (Pred Acc: 88.6%); and, (2) select an approximate next-best action for the block stacking task, for execution by an integrated robot system, achieving 94.2% task success rate. We also demonstrate our framework's suitability for real-world robot systems by demonstrating successful task executions with a domestic support robot, with perception and manipulation sub-system integration. Hence, we show that by embedding physics-based causal reasoning into robots' decision-making processes, we can make robot task execution safer, more reliable, and more robust to various types of uncertainty.

Algorithms with predictions have attracted much attention in the last years across various domains, including variants of facility location, as a way to surpass traditional worst-case analyses. We study the $k$-facility location mechanism design problem, where the $n$ agents are strategic and might misreport their location. Unlike previous models, where predictions are for the $k$ optimal facility locations, we receive $n$ predictions for the locations of each of the agents. However, these predictions are only "mostly" and "approximately" correct (or MAC for short) -- i.e., some $\delta$-fraction of the predicted locations are allowed to be arbitrarily incorrect, and the remainder of the predictions are allowed to be correct up to an $\varepsilon$-error. We make no assumption on the independence of the errors. Can such predictions allow us to beat the current best bounds for strategyproof facility location? We show that the $1$-median (geometric median) of a set of points is naturally robust under corruptions, which leads to an algorithm for single-facility location with MAC predictions. We extend the robustness result to a "balanced" variant of the $k$ facilities case. Without balancedness, we show that robustness completely breaks down, even for the setting of $k=2$ facilities on a line. For this "unbalanced" setting, we devise a truthful random mechanism that outperforms the best known result of Lu et al. [2010], which does not use predictions. En route, we introduce the problem of "second" facility location (when the first facility's location is already fixed). Our findings on the robustness of the $1$-median and more generally $k$-medians may be of independent interest, as quantitative versions of classic breakdown-point results in robust statistics.

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.

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,?].