When predicting physical phenomena through simulation, quantification of the total uncertainty due to multiple sources is as crucial as making sure the underlying numerical model is accurate. Possible sources include irreducible aleatoric uncertainty due to noise in the data, epistemic uncertainty induced by insufficient data or inadequate parameterization, and model-form uncertainty related to the use of misspecified model equations. Physics-based regularization interacts in nontrivial ways with aleatoric, epistemic and model-form uncertainty and their combination, and a better understanding of this interaction is needed to improve the predictive performance of physics-informed digital twins that operate under real conditions. With a specific focus on biological and physiological models, this study investigates the decomposition of total uncertainty in the estimation of states and parameters of a differential system simulated with MC X-TFC, a new physics-informed approach for uncertainty quantification based on random projections and Monte-Carlo sampling. MC X-TFC is applied to a six-compartment stiff ODE system, the CVSim-6 model, developed in the context of human physiology. The system is analyzed by progressively removing data while estimating an increasing number of parameters and by investigating total uncertainty under model-form misspecification of non-linear resistance in the pulmonary compartment. In particular, we focus on the interaction between the formulation of the discrepancy term and quantification of model-form uncertainty, and show how additional physics can help in the estimation process. The method demonstrates robustness and efficiency in estimating unknown states and parameters, even with limited, sparse, and noisy data. It also offers great flexibility in integrating data with physics for improved estimation, even in cases of model misspecification.

Accurately predicting the long-term behavior of chaotic systems is crucial for various applications such as climate modeling. However, achieving such predictions typically requires iterative computations over a dense spatiotemporal grid to account for the unstable nature of chaotic systems, which is expensive and impractical in many real-world situations. An alternative approach to such a full-resolved simulation is using a coarse grid and then correcting its errors through a \textit{closure model}, which approximates the overall information from fine scales not captured in the coarse-grid simulation. Recently, ML approaches have been used for closure modeling, but they typically require a large number of training samples from expensive fully-resolved simulations (FRS). In this work, we prove an even more fundamental limitation, i.e., the standard approach to learning closure models suffers from a large approximation error for generic problems, no matter how large the model is, and it stems from the non-uniqueness of the mapping. We propose an alternative end-to-end learning approach using a physics-informed neural operator (PINO) that overcomes this limitation by not using a closure model or a coarse-grid solver. We first train the PINO model on data from a coarse-grid solver and then fine-tune it with (a small amount of) FRS and physics-based losses on a fine grid. The discretization-free nature of neural operators means that they do not suffer from the restriction of a coarse grid that closure models face, and they can provably approximate the long-term statistics of chaotic systems. In our experiments, our PINO model achieves a 120x speedup compared to FRS with a relative error $\sim 5\%$. In contrast, the closure model coupled with a coarse-grid solver is $58$x slower than PINO while having a much higher error $\sim205\%$ when the closure model is trained on the same FRS dataset.

Minimum Bayes risk (MBR) decoding is a decision rule of text generation tasks that outperforms conventional maximum a posterior (MAP) decoding using beam search by selecting high-quality outputs based on a utility function rather than those with high-probability. Typically, it finds the most suitable hypothesis from the set of hypotheses under the sampled pseudo-references. mbrs is a library of MBR decoding, which can flexibly combine various metrics, alternative expectation estimations, and algorithmic variants. It is designed with a focus on speed measurement and calling count of code blocks, transparency, reproducibility, and extensibility, which are essential for researchers and developers. We published our mbrs as an MIT-licensed open-source project, and the code is available on GitHub. GitHub: https://github.com/naist-nlp/mbrs

In the ride-hailing industry, subsidies are predominantly employed to incentivize consumers to place more orders, thereby fostering market growth. Causal inference techniques are employed to estimate the consumer elasticity with different subsidy levels. However, the presence of confounding effects poses challenges in achieving an unbiased estimate of the uplift effect. We introduce a consumer subsidizing system to capture relationships between subsidy propensity and the treatment effect, which proves effective while maintaining a lightweight online environment.

In robotic inspection of aviation parts, achieving accurate pairwise point cloud registration between scanned and model data is essential. However, noise and outliers generated in robotic scanned data can compromise registration accuracy. To mitigate this challenge, this article proposes a probability-based registration method utilizing Gaussian Mixture Model (GMM) with local consistency constraint. This method converts the registration problem into a model fitting one, constraining the similarity of posterior distributions between neighboring points to enhance correspondence robustness. We employ the Expectation Maximization algorithm iteratively to find optimal rotation matrix and translation vector while obtaining GMM parameters. Both E-step and M-step have closed-form solutions. Simulation and actual experiments confirm the method's effectiveness, reducing root mean square error by 20% despite the presence of noise and outliers. The proposed method excels in robustness and accuracy compared to existing methods.

Recent advancements in physics-based character animation leverage deep learning to generate agile and natural motion, enabling characters to execute movements such as backflips, boxing, and tennis. However, reproducing the selection and use of diverse motor skills in dynamic environments to solve complex tasks, as humans do, still remains a challenge. We present a strategy and skill learning approach for physics-based table tennis animation. Our method addresses the issue of mode collapse, where the characters do not fully utilize the motor skills they need to perform to execute complex tasks. More specifically, we demonstrate a hierarchical control system for diversified skill learning and a strategy learning framework for effective decision-making. We showcase the efficacy of our method through comparative analysis with state-of-the-art methods, demonstrating its capabilities in executing various skills for table tennis. Our strategy learning framework is validated through both agent-agent interaction and human-agent interaction in Virtual Reality, handling both competitive and cooperative tasks.

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.

Compared to physics-based computational manufacturing, data-driven models such as machine learning (ML) are alternative approaches to achieve smart manufacturing. However, the data-driven ML's "black box" nature has presented a challenge to interpreting its outcomes. On the other hand, governing physical laws are not effectively utilized to develop data-efficient ML algorithms. To leverage the advantages of ML and physical laws of advanced manufacturing, this paper focuses on the development of a physics-informed machine learning (PIML) model by integrating neural networks and physical laws to improve model accuracy, transparency, and generalization with case studies in laser metal deposition (LMD).

Physically-simulated models for human motion can generate high-quality responsive character animations, often in real-time. Natural language serves as a flexible interface for controlling these models, allowing expert and non-expert users to quickly create and edit their animations. Many recent physics-based animation methods, including those that use text interfaces, train control policies using reinforcement learning (RL). However, scaling these methods beyond several hundred motions has remained challenging. Meanwhile, kinematic animation models are able to successfully learn from thousands of diverse motions by leveraging supervised learning methods. Inspired by these successes, in this work we introduce SuperPADL, a scalable framework for physics-based text-to-motion that leverages both RL and supervised learning to train controllers on thousands of diverse motion clips. SuperPADL is trained in stages using progressive distillation, starting with a large number of specialized experts using RL. These experts are then iteratively distilled into larger, more robust policies using a combination of reinforcement learning and supervised learning. Our final SuperPADL controller is trained on a dataset containing over 5000 skills and runs in real time on a consumer GPU. Moreover, our policy can naturally transition between skills, allowing for users to interactively craft multi-stage animations. We experimentally demonstrate that SuperPADL significantly outperforms RL-based baselines at this large data scale.

High-performance computing (HPC) has revolutionized our ability to perform detailed simulations of complex real-world processes. A prominent contemporary example is from aerospace propulsion, where HPC is used for rotating detonation rocket engine (RDRE) simulations in support of the design of next-generation rocket engines; however, these simulations take millions of core hours even on powerful supercomputers, which makes them impractical for engineering tasks like design exploration and risk assessment. Reduced-order models (ROMs) address this limitation by constructing computationally cheap yet sufficiently accurate approximations that serve as surrogates for the high-fidelity model. This paper contributes a new distributed algorithm that achieves fast and scalable construction of predictive physics-based ROMs trained from sparse datasets of extremely large state dimension. The algorithm learns structured physics-based ROMs that approximate the dynamical systems underlying those datasets. This enables model reduction for problems at a scale and complexity that exceeds the capabilities of existing approaches. We demonstrate our algorithm's scalability using up to $2,048$ cores on the Frontera supercomputer at the Texas Advanced Computing Center. We focus on a real-world three-dimensional RDRE for which one millisecond of simulated physical time requires one million core hours on a supercomputer. Using a training dataset of $2,536$ snapshots each of state dimension $76$ million, our distributed algorithm enables the construction of a predictive data-driven reduced model in just $13$ seconds on $2,048$ cores on Frontera.