This study presents domain-informed genetic superposition programming (DIGSP), a symbolic regression framework tailored for engineering systems governed by separable physical mechanisms. DIGSP partitions the input space into domain-specific feature subsets and evolves independent genetic programming (GP) populations to model material-specific effects. Early evolution occurs in isolation, while ensemble fitness promotes inter-population cooperation. To enable symbolic superposition, an adaptive hierarchical symbolic abstraction mechanism (AHSAM) is triggered after stagnation across all populations. AHSAM performs analysis of variance- (ANOVA) based filtering to identify statistically significant individuals, compresses them into symbolic constructs, and injects them into all populations through a validation-guided pruning cycle. The DIGSP is benchmarked against a baseline multi-gene genetic programming (BGP) model using a dataset of steel fiber-reinforced concrete (SFRC) beams. Across 30 independent trials with 65% training, 10% validation, and 25% testing splits, DIGSP consistently outperformed BGP in training and test root mean squared error (RMSE). The Wilcoxon rank-sum test confirmed statistical significance (p < 0.01), and DIGSP showed tighter error distributions and fewer outliers. No significant difference was observed in validation RMSE due to limited sample size. These results demonstrate that domain-informed structural decomposition and symbolic abstraction improve convergence and generalization. DIGSP offers a principled and interpretable modeling strategy for systems where symbolic superposition aligns with the underlying physical structure.

The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic regression. However, existing approaches are dominated by heuristic algorithms or data-hungry black-box methods, which often demand low-noise settings and lack principled uncertainty quantification. Motivated by interpretable Statistical Artificial Intelligence, we develop a hierarchical Bayesian framework for symbolic regression that represents scientific laws as ensembles of tree-structured symbolic expressions endowed with a regularized tree prior. This coherent probabilistic formulation enables full posterior inference via an efficient Markov chain Monte Carlo algorithm, yielding a balance between predictive accuracy and structural parsimony. To guide symbolic model selection, we develop a marginal posterior-based criterion adhering to the Occam's window principle and further quantify structural fidelity to ground truth through a tailored expression-distance metric. On the theoretical front, we establish near-minimax rate of Bayesian posterior concentration, providing the first rigorous guarantee in context of symbolic regression. Empirical evaluation demonstrates robust performance of our proposed methodology against state-of-the-art competing modules on a simulated example, a suite of canonical Feynman equations, and single-atom catalysis dataset.

Accurate modeling of personalized cardiovascular dynamics is crucial for non-invasive monitoring and therapy planning. State-of-the-art physics-informed neural network (PINN) approaches employ deep, multi-branch architectures with adversarial or contrastive objectives to enforce partial differential equation constraints. While effective, these enhancements introduce significant training and implementation complexity, limiting scalability and practical deployment. We investigate physics-informed neural operator learning models as efficient supervisory signals for training simplified architectures through knowledge distillation. Our approach pre-trains a physics-informed DeepONet (PI-DeepONet) on high-fidelity cuffless blood pressure recordings to learn operator mappings from raw wearable waveforms to beat-to-beat pressure signals under embedded physics constraints. This pre-trained operator serves as a frozen supervisor in a lightweight knowledge-distillation pipeline, guiding streamlined base models that eliminate complex adversarial and contrastive learning components while maintaining performance. We characterize the role of physics-informed regularization in operator learning and demonstrate its effectiveness for supervisory guidance. Through extensive experiments, our operator-supervised approach achieves performance parity with complex baselines (correlation: 0.766 vs. 0.770, RMSE: 4.452 vs. 4.501), while dramatically reducing architectural complexity from eight critical hyperparameters to a single regularization coefficient and decreasing training overhead by 4%. Our results demonstrate that operator-based supervision effectively replaces intricate multi-component training strategies, offering a more scalable and interpretable approach to physiological modeling with reduced implementation burden.

Inferring parameters of high-dimensional partial differential equations (PDEs) poses significant computational and inferential challenges, primarily due to the curse of dimensionality and the inherent limitations of traditional numerical methods. This paper introduces a novel two-stage Bayesian framework that synergistically integrates training, physics-based deep kernel learning (DKL) with Hamiltonian Monte Carlo (HMC) to robustly infer unknown PDE parameters and quantify their uncertainties from sparse, exact observations. The first stage leverages physics-based DKL to train a surrogate model, which jointly yields an optimized neural network feature extractor and robust initial estimates for the PDE parameters. In the second stage, with the neural network weights fixed, HMC is employed within a full Bayesian framework to efficiently sample the joint posterior distribution of the kernel hyperparameters and the PDE parameters. Numerical experiments on canonical and high-dimensional inverse PDE problems demonstrate that our framework accurately estimates parameters, provides reliable uncertainty estimates, and effectively addresses challenges of data sparsity and model complexity, offering a robust and scalable tool for diverse scientific and engineering applications.

Demands for software-defined vehicles (SDV) are rising and electric vehicles (EVs) are increasingly being equipped with powerful computers. This enables onboard AI systems to optimize charge-aware path optimization customized to reflect vehicle's current condition and environment. We present VEGA, a charge-aware EV navigation agent that plans over a charger-annotated road graph using Proximal Policy Optimization (PPO) with budgeted A* teacher-student guidance under state-of-charge (SoC) feasibility. VEGA consists of two modules. First, a physics-informed neural operator (PINO), trained on real vehicle speed and battery-power logs, uses recent vehicle speed logs to estimate aerodynamic drag, rolling resistance, mass, motor and regenerative-braking efficiencies, and auxiliary load by learning a vehicle-custom dynamics. Second, a Reinforcement Learning (RL) agent uses these dynamics to optimize a path with optimal charging stops and dwell times under SoC constraints. VEGA requires no additional sensors and uses only vehicle speed signals. It may serve as a virtual sensor for power and efficiency to potentially reduce EV cost. In evaluation on long routes like San Francisco to New York, VEGA's stops, dwell times, SoC management, and total travel time closely track Tesla Trip Planner while being slightly more conservative, presumably due to real vehicle conditions such as vehicle parameter drift due to deterioration. Although trained only in U.S. regions, VEGA was able to compute optimal charge-aware paths in France and Japan, demonstrating generalizability. It achieves practical integration of physics-informed learning and RL for EV eco-routing.

Continuum robots are advancing bronchoscopy procedures by accessing complex lung airways and enabling targeted interventions. However, their development is limited by the lack of realistic training and test environments: Real data is difficult to collect due to ethical constraints and patient safety concerns, and developing autonomy algorithms requires realistic imaging and physical feedback. We present ROOM (Realistic Optical Observation in Medicine), a comprehensive simulation framework designed for generating photorealistic bronchoscopy training data. By leveraging patient CT scans, our pipeline renders multi-modal sensor data including RGB images with realistic noise and light specularities, metric depth maps, surface normals, optical flow and point clouds at medically relevant scales. We validate the data generated by ROOM in two canonical tasks for medical robotics -- multi-view pose estimation and monocular depth estimation, demonstrating diverse challenges that state-of-the-art methods must overcome to transfer to these medical settings. Furthermore, we show that the data produced by ROOM can be used to fine-tune existing depth estimation models to overcome these challenges, also enabling other downstream applications such as navigation. We expect that ROOM will enable large-scale data generation across diverse patient anatomies and procedural scenarios that are challenging to capture in clinical settings. Code and data: https://github.com/iamsalvatore/room.

Minimum Bayes risk (MBR) decoding is a decision rule of text generation, which selects the hypothesis that maximizes the expected utility and robustly generates higher-quality texts than maximum a posteriori (MAP) decoding. However, it depends on sample texts drawn from the text generation model; thus, it is difficult to find a hypothesis that correctly captures the knowledge or information of out-of-domain. To tackle this issue, we propose case-based decision-theoretic (CBDT) decoding, another method to estimate the expected utility using examples of domain data. CBDT decoding not only generates higher-quality texts than MAP decoding, but also the combination of MBR and CBDT decoding outperformed MBR decoding in seven domain De--En and Ja$\leftrightarrow$En translation tasks and image captioning tasks on MSCOCO and nocaps datasets.

Potential failures of physics-informed machine learning in traffic flow modeling: theoretical and experimental analysis Yuan-Zheng Lei a, Yaobang Gong a, Dianwei Chen a, Yao Cheng b, Xianfeng Terry Yang* a a University of Maryland, College Park, MD 20742, United States b Florida Atlantic University, Boca Raton, FL 33431, United StatesAbstract This study investigates why physics-informed machine learning (PIML) may fail when it comes to macroscopic traffic flow modeling. We define failure as the case where a PIML model underperforms both its purely data-driven and purely physics-based counterparts by a given threshold. Our analysis shows that physics residuals themselves do not inherently hinder the optimization of the loss function, which is a main reason responsible for the failure of the PIML model in other fields. Instead, successful parameter updates require both machine-learning and physics gradients to form acute angles with the true gradient. Our experiment shows that this condition may be hard to achieve for PIML under a general low-resolution loop dataset. In particular, when the traffic data resolution is low, a neural network cannot accurately approximate density and speed, causing the constructed physics residuals, already affected by discrete sampling and temporal averaging, to lose their ability to reflect the actual PDE dynamics. This degradation can directly lead to PIML failure. From a theoretical standpoint, we show that although the exact solutions of the LWR and ARZ models are weak solutions, for piecewise C k initial data and under mild conditions, the solutions remain C k on the complement of the shock set over finite time, with only finitely many shock waves, where C k refers to k times continuously differentiable. Since the shock set has Lebesgue measure zero, the probability of a detector measurement or auxiliary collocation point lying exactly on a discontinuity is essentially zero; asymptotically, every auxiliary point admits a sufficiently small smooth neighborhood where the physics residual is well-defined and valid. Consequently, the well-known limitation that MLPs cannot exactly represent non-smooth functions does not materially affect our setting, as the residual evaluation almost always occurs in smooth regions. We also investigate the error lower bounds of the MSE of physics residuals for PIML models under high-resolution data. We prove that higher-order models like ARZ possess strictly larger consistency error lower bounds than lower-order models like LWR under mild conditions.