The mass loss of the polar ice sheets contributes considerably to ongoing sea-level rise and changing ocean circulation, leading to coastal flooding and risking the homes and livelihoods of tens of millions of people globally. To address the complex problem of ice behavior, physical models and data-driven models have been proposed in the literature. Although traditional physical models can guarantee physically meaningful results, they have limitations in producing high-resolution results. On the other hand, data-driven approaches require large amounts of high-quality and labeled data, which is rarely available in the polar regions. Hence, as a promising framework that leverages the advantages of physical models and data-driven methods, physics-informed machine learning (PIML) has been widely studied in recent years. In this paper, we review the existing algorithms of PIML, provide our own taxonomy based on the methods of combining physics and data-driven approaches, and analyze the advantages of PIML in the aspects of accuracy and efficiency. Further, our survey discusses some current challenges and highlights future opportunities, including PIML on sea ice studies, PIML with different combination methods and backbone networks, and neural operator methods.

Searching dependency graphs and manipulating them can be a time consuming and challenging task to get right. We document Semgrex, a system for searching dependency graphs, and introduce Ssurgeon, a system for manipulating the output of Semgrex. The compact language used by these systems allows for easy command line or API processing of dependencies. Additionally, integration with publicly released toolkits in Java and Python allows for searching text relations and attributes over natural text.

We propose a constraint-based algorithm, which automatically determines causal relevance thresholds, to infer causal networks from data. We call these topological thresholds. We present two methods for determining the threshold: the first seeks a set of edges that leaves no disconnected nodes in the network; the second seeks a causal large connected component in the data. We tested these methods both for discrete synthetic and real data, and compared the results with those obtained for the PC algorithm, which we took as the benchmark. We show that this novel algorithm is generally faster and more accurate than the PC algorithm. The algorithm for determining the thresholds requires choosing a measure of causality. We tested our methods for Fisher Correlations, commonly used in PC algorithm (for instance in \cite{kalisch2005}), and further proposed a discrete and asymmetric measure of causality, that we called Net Influence, which provided very good results when inferring causal networks from discrete data. This metric allows for inferring directionality of the edges in the process of applying the thresholds, speeding up the inference of causal DAGs.

Realistic object interactions are crucial for creating immersive virtual experiences, yet synthesizing realistic 3D object dynamics in response to novel interactions remains a significant challenge. Unlike unconditional or text-conditioned dynamics generation, action-conditioned dynamics requires perceiving the physical material properties of objects and grounding the 3D motion prediction on these properties, such as object stiffness. However, estimating physical material properties is an open problem due to the lack of material ground-truth data, as measuring these properties for real objects is highly difficult. We present Phys-Dreamer, a physics-based approach that endows static 3D objects with interactive dynamics by leveraging the object dynamics priors learned by video generation models. By distilling these priors, PhysDreamer enables the synthesis of realistic object responses to novel interactions, such as external forces or agent manipulations. We demonstrate our approach on diverse examples of elastic objects and evaluate the realism of the synthesized interactions through a user study. PhysDreamer takes a step towards more engaging and realistic virtual experiences by enabling static 3D objects to dynamically respond to interactive stimuli in a physically plausible manner. See our project page at https: //physdreamer.github.io/.

We present a unified framework called deep dependency networks (DDNs) that combines dependency networks and deep learning architectures for multi-label classification, with a particular emphasis on image and video data. The primary advantage of dependency networks is their ease of training, in contrast to other probabilistic graphical models like Markov networks. In particular, when combined with deep learning architectures, they provide an intuitive, easy-to-use loss function for multi-label classification. A drawback of DDNs compared to Markov networks is their lack of advanced inference schemes, necessitating the use of Gibbs sampling. To address this challenge, we propose novel inference schemes based on local search and integer linear programming for computing the most likely assignment to the labels given observations. We evaluate our novel methods on three video datasets (Charades, TACoS, Wetlab) and three image datasets (MS-COCO, PASCAL VOC, NUS-WIDE), comparing their performance with (a) basic neural architectures and (b) neural architectures combined with Markov networks equipped with advanced inference and learning techniques. Our results demonstrate the superiority of our new DDN methods over the two competing approaches.

In April 2021 Stava bridge, a main bridge on E6 in Norway, was abruptly closed for traffic. A structural defect had seriously compromised the bridge structural integrity. The Norwegian Public Roads Administration (NPRA) closed it, made a temporary solution and reopened with severe traffic restrictions. The incident was alerted through what constitutes the bridge Digital Twin processing data from Internet of Things sensors. The solution was crucial in online and offline diagnostics, the case demonstrating the value of technologies to tackle emerging dangerous situations as well as acting preventively. A critical and rapidly developing damage was detected in time to stop the development, but not in time to avoid the incident altogether. The paper puts risk in a broader perspective for an organization responsible for highway infrastructure. It positions online monitoring and Digital Twins in the context of Risk- and Condition-Based Maintenance. The situation that arose at Stava bridge, and how it was detected, analyzed, and diagnosed during virtual inspection, is described. The case demonstrates how combining physics-based methods with Machine Learning can facilitate damage detection and diagnostics. A summary of lessons learnt, both from technical and organizational perspectives, as well as plans of future work, is presented.

Uncertainty quantification (UQ) in scientific machine learning (SciML) combines the powerful predictive power of SciML with methods for quantifying the reliability of the learned models. However, two major challenges remain: limited interpretability and expensive training procedures. We provide a new interpretation for UQ problems by establishing a new theoretical connection between some Bayesian inference problems arising in SciML and viscous Hamilton-Jacobi partial differential equations (HJ PDEs). Namely, we show that the posterior mean and covariance can be recovered from the spatial gradient and Hessian of the solution to a viscous HJ PDE. As a first exploration of this connection, we specialize to Bayesian inference problems with linear models, Gaussian likelihoods, and Gaussian priors. In this case, the associated viscous HJ PDEs can be solved using Riccati ODEs, and we develop a new Riccati-based methodology that provides computational advantages when continuously updating the model predictions. Specifically, our Riccati-based approach can efficiently add or remove data points to the training set invariant to the order of the data and continuously tune hyperparameters. Moreover, neither update requires retraining on or access to previously incorporated data. We provide several examples from SciML involving noisy data and \textit{epistemic uncertainty} to illustrate the potential advantages of our approach. In particular, this approach's amenability to data streaming applications demonstrates its potential for real-time inferences, which, in turn, allows for applications in which the predicted uncertainty is used to dynamically alter the learning process.

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.