This work presents a physics-based machine learning framework to predict and analyze oxides of nitrogen (NOx) emissions from compression-ignition engine-powered vehicles using on-board diagnostics (OBD) data as input. Accurate NOx prediction from OBD datasets is difficult because NOx formation inside an engine combustion chamber is governed by complex processes occurring on timescales much shorter than the data collection rate. Thus, emissions generally cannot be predicted accurately using simple empirically derived physics models. Black box models like genetic algorithms or neural networks can be more accurate, but have poor interpretability. The transparent model presented in this paper has both high accuracy and can explain potential sources of high emissions. The proposed framework consists of two major steps: a physics-based NOx prediction model combined with a novel Divergent Window Co-occurrence (DWC) Pattern detection algorithm to analyze operating conditions that are not adequately addressed by the physics-based model. The proposed framework is validated for generalizability with a second vehicle OBD dataset, a sensitivity analysis is performed, and model predictions are compared with that from a deep neural network. The results show that NOx emissions predictions using the proposed model has around 55% better root mean square error, and around 60% higher mean absolute error compared to the baseline NOx prediction model from previously published work. The DWC Pattern Detection Algorithm identified low engine power conditions to have high statistical significance, indicating an operating regime where the model can be improved. This work shows that the physics-based machine learning framework is a viable method for predicting NOx emissions from engines that do not incorporate NOx sensing.

Accurate lifetime prediction of structures subjected to cyclic loading is vital, especially in scenarios involving non-uniform loading histories where load sequencing critically influences structural durability. Addressing this complexity requires advanced modeling approaches capable of capturing the intricate relationship between loading sequences and fatigue lifetime. Traditional fatigue simulations are computationally prohibitive, necessitating more efficient methods. This study highlights the potential of physics-based machine learning ($\phi$ML) to predict the fatigue lifetime of materials. Specifically, a FFNN is designed to embed physical constraints from experimental evidence directly into its architecture to enhance prediction accuracy. It is trained using numerical simulations generated by a physically based anisotropic continuum damage fatigue model. The model is calibrated and validated against experimental fatigue data of concrete cylinder specimens tested in uniaxial compression. The proposed approach demonstrates superior accuracy compared to purely data-driven neural networks, particularly in situations with limited training data, achieving realistic predictions of damage accumulation. Thus, a general algorithm is developed and successfully applied to predict fatigue lifetimes under complex loading scenarios with multiple loading ranges. Hereby, the $\phi$ML model serves as a surrogate to capture damage evolution across load transitions. The $\phi$ML based algorithm is subsequently employed to investigate the influence of multiple loading transitions on accumulated fatigue life, and its predictions align with trends observed in recent experimental studies. This work demonstrates $\phi$ML as a promising technique for efficient and reliable fatigue life prediction in engineering structures, with possible integration into digital twin models for real-time assessment.

The deployment of autonomous navigation systems on ships necessitates accurate motion prediction models tailored to individual vessels. Traditional physics-based models, while grounded in hydrodynamic principles, often fail to account for ship-specific behaviors under real-world conditions. Conversely, purely data-driven models offer specificity but lack interpretability and robustness in edge cases. This study proposes a data-driven physics-based model that integrates physics-based equations with data-driven parameter optimization, leveraging the strengths of both approaches to ensure interpretability and adaptability. The model incorporates physics-based components such as 3-DoF dynamics, rudder, and propeller forces, while parameters such as resistance curve and rudder coefficients are optimized using synthetic data. By embedding domain knowledge into the parameter optimization process, the fitted model maintains physical consistency. Validation of the approach is realized with two container ships by comparing, both qualitatively and quantitatively, predictions against ground-truth trajectories. The results demonstrate significant improvements, in predictive accuracy and reliability, of the data-driven physics-based models over baseline physics-based models tuned with traditional marine engineering practices. The fitted models capture ship-specific behaviors in diverse conditions with their predictions being, 51.6% (ship A) and 57.8% (ship B) more accurate, 72.36% (ship A) and 89.67% (ship B) more consistent.

We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational cost, in terms of training procedures. Our approach is mathematically interpretable and backed by rigorous theoretical guarantees in the form of quantitative worst-case error bounds for the learned equation. Numerical benchmarks demonstrate significant improvements in computational complexity and robustness while achieving one to two orders of magnitude improvements in terms of accuracy compared to state-of-the-art algorithms. Significance statement We present a novel algorithm inspired by kernel methods and Gaussian processes for learning differential equations and their solution operators in scarce data regimes. Our approach: (a) is significantly more efficient than state-of-the-art methods, including neural networks, in terms of required data and computational time. In fact, we obtain one to two orders of magnitude improvement in accuracy on a number of benchmarks; (b) is supported by rigorous theory featuring the first quantitative worst-case error bounds for equation learning; and (c) can solve previously intractable scientific computing problems such as one-shot operator learning and learning of variable-coefficient PDEs in extremely scarce data regimes.

Representing 3D scenes from multiview images is a core challenge in computer vision and graphics, which requires both precise rendering and accurate reconstruction. Recently, 3D Gaussian Splatting (3DGS) has garnered significant attention for its high-quality rendering and fast inference speed. Yet, due to the unstructured and irregular nature of Gaussian point clouds, ensuring accurate geometry reconstruction remains difficult. Existing methods primarily focus on geometry regularization, with common approaches including primitive-based and dual-model frameworks. However, the former suffers from inherent conflicts between rendering and reconstruction, while the latter is computationally and storage-intensive. To address these challenges, we propose CarGS, a unified model leveraging Contribution-adaptive regularization to achieve simultaneous, high-quality rendering and surface reconstruction. The essence of our framework is learning adaptive contribution for Gaussian primitives by squeezing the knowledge from geometry regularization into a compact MLP. Additionally, we introduce a geometry-guided densification strategy with clues from both normals and Signed Distance Fields (SDF) to improve the capability of capturing high-frequency details. Our design improves the mutual learning of the two tasks, meanwhile its unified structure does not require separate models as in dual-model based approaches, guaranteeing efficiency. Extensive experiments demonstrate the ability to achieve state-of-the-art (SOTA) results in both rendering fidelity and reconstruction accuracy while maintaining real-time speed and minimal storage size.

Achieving realistic simulations of humans interacting with a wide range of objects has long been a fundamental goal. Extending physics-based motion imitation to complex human-object interactions (HOIs) is challenging due to intricate human-object coupling, variability in object geometries, and artifacts in motion capture data, such as inaccurate contacts and limited hand detail. We introduce InterMimic, a framework that enables a single policy to robustly learn from hours of imperfect MoCap data covering diverse full-body interactions with dynamic and varied objects. Our key insight is to employ a curriculum strategy -- perfect first, then scale up. We first train subject-specific teacher policies to mimic, retarget, and refine motion capture data. Next, we distill these teachers into a student policy, with the teachers acting as online experts providing direct supervision, as well as high-quality references. Notably, we incorporate RL fine-tuning on the student policy to surpass mere demonstration replication and achieve higher-quality solutions. Our experiments demonstrate that InterMimic produces realistic and diverse interactions across multiple HOI datasets. The learned policy generalizes in a zero-shot manner and seamlessly integrates with kinematic generators, elevating the framework from mere imitation to generative modeling of complex human-object interactions.

Scientific machine learning (SciML) integrates machine learning (ML) into scientific workflows to enhance system simulation and analysis, with an emphasis on computational modeling of physical systems. This field emerged from Department of Energy workshops and initiatives starting in 2018, which also identified the need to increase "the scale, rigor, robustness, and reliability of SciML necessary for routine use in science and engineering applications" [5]. The field's subsequent growth through funding initiatives, conference themes, and high-profile publications stems from its ability to unite ML's predictive power with the domain knowledge and mathematical rigor of computational science and engineering (CSE). However, this surge in SciML development has outpaced good practices and reporting standards for building trust [66, 51, 109, 117]. SciML models must demonstrate trustworthiness to be safe and useful [44]. Organizational and computational trust definitions [92, 106] inform our criteria for trustworthy SciML: competence in basic performance, reliability across conditions, transparency about processes and limitations, and alignment with scientific objectives. These criteria span technical attributes (correctness, reliability, safety) and human-centric qualities (comprehensibility, transparency).

A comprehensive understanding of causality is critical for navigating and operating within today's complex real-world systems. The absence of realistic causal models with known data generating processes complicates fair benchmarking. In this paper, we present the CausalMan simulator, modeled after a real-world production line. The simulator features a diverse range of linear and non-linear mechanisms and challenging-to-predict behaviors, such as discrete mode changes. We demonstrate the inadequacy of many state-of-the-art approaches and analyze the significant differences in their performance and tractability, both in terms of runtime and memory complexity. As a contribution, we will release the CausalMan large-scale simulator. We present two derived datasets, and perform an extensive evaluation of both.

Shallow water equations (SWEs) are the backbone of most hydrodynamics models for flood prediction, river engineering, and many other water resources applications. The estimation of flow resistance, i.e., the Manning's roughness coefficient $n$, is crucial for ensuring model accuracy, and has been previously determined using empirical formulas or tables. To better account for temporal and spatial variability in channel roughness, inverse modeling of $n$ using observed flow data is more reliable and adaptable; however, it is challenging when using traditional SWE solvers. Based on the concept of universal differential equation (UDE), which combines physics-based differential equations with neural networks (NNs), we developed a universal SWEs (USWEs) solver, Hydrograd, for hybrid hydrodynamics modeling. It can do accurate forward simulations, support automatic differentiation (AD) for gradient-based sensitivity analysis and parameter inversion, and perform scientific machine learning for physics discovery. In this work, we first validated the accuracy of its forward modeling, then applied a real-world case to demonstrate the ability of USWEs to capture model sensitivity (gradients) and perform inverse modeling of Manning's $n$. Furthermore, we used a NN to learn a universal relationship between $n$, hydraulic parameters, and flow in a real river channel. Unlike inverse modeling using surrogate models, Hydrograd uses a two-dimensional SWEs solver as its physics backbone, which eliminates the need for data-intensive pretraining and resolves the generalization problem when applied to out-of-sample scenarios. This differentiable modeling approach, with seamless integration with NNs, provides a new pathway for solving complex inverse problems and discovering new physics in hydrodynamics.

Large language models demonstrate remarkable capabilities across various domains, especially mathematics and logic reasoning. However, current evaluations overlook physics-based reasoning - a complex task requiring physics theorems and constraints. We present PhysReason, a 1,200-problem benchmark comprising knowledge-based (25%) and reasoning-based (75%) problems, where the latter are divided into three difficulty levels (easy, medium, hard). Notably, problems require an average of 8.1 solution steps, with hard requiring 15.6, reflecting the complexity of physics-based reasoning. We propose the Physics Solution Auto Scoring Framework, incorporating efficient answer-level and comprehensive step-level evaluations. Top-performing models like Deepseek-R1, Gemini-2.0-Flash-Thinking, and o3-mini-high achieve less than 60% on answer-level evaluation, with performance dropping from knowledge questions (75.11%) to hard problems (31.95%). Through step-level evaluation, we identified four key bottlenecks: Physics Theorem Application, Physics Process Understanding, Calculation, and Physics Condition Analysis. These findings position PhysReason as a novel and comprehensive benchmark for evaluating physics-based reasoning capabilities in large language models. Our code and data will be published at https:/dxzxy12138.github.io/PhysReason.