physics-informed analysis

In scientific machine learning, learned features often lack physical interpretability and meaningful mechanistic grounding. Method: We propose a physics-informed nonlinear feature construction paradigm that integrates dimensional analysis with domain-specific physical constraints to enforce physical consistency in the feature mapping; it employs feature importance ranking to identify dominant physical mechanisms and supports governing-equation discovery and novel physical relation inference when first-principles laws are unknown. Contribution/Results: Experiments across multiple scientific datasets demonstrate significant improvements in regression accuracy and classification skill scores, while simultaneously achieving enhanced interpretability and mechanistic insight. The framework provides a generalizable, interpretable machine learning approach for scientific discovery—bridging data-driven modeling with physical understanding.

Addressing the dual challenges of physical inconsistency and poor generalization under limited data, this work introduces a novel paradigm that projects model outputs onto a physics-defined manifold. Specifically, predictions are explicitly projected onto a differential-geometric manifold constrained by prior physical laws—such as conservation principles—ensuring inherent compliance with physical constraints. The method is architecture-agnostic and task-agnostic, overcoming the unreliable generalization of penalty-based approaches and the inflexibility of physics-invariant architectures. By integrating implicit constraint enforcement (e.g., via Lagrange multipliers) with a plug-and-play interface, it seamlessly interoperates with Physics-Informed Neural Networks (PINNs). Evaluated on benchmark tasks—including a spring-mass oscillator and low-temperature reactive plasma modeling—the approach reduces physical law violation rates by 92% and decreases prediction error of key state variables by 37%. Under scarce-data regimes, it significantly outperforms both standard PINNs and purely data-driven models.

This work addresses the binary classification problem of experimental feasibility for Higgs boson observables in high-energy physics. We systematically benchmark XGBoost, Random Forest, AdaBoost, Quadratic Discriminant Analysis (QDA), standard neural networks, and Physics-Informed Neural Networks (PINNs). To our knowledge, this is the first evaluation of XGBoost–PINN synergy in particle physics. We propose a novel PINN architecture explicitly embedding Higgs-specific physical constraints and introduce a two-stage modeling strategy: XGBoost performs rapid initial screening on limited data, while PINN delivers high-accuracy, physically consistent final classification. Results show that XGBoost achieves the fastest training, whereas PINN attains superior classification accuracy and strict adherence to physical conservation laws. The study quantitatively elucidates the fundamental trade-off among predictive accuracy, computational efficiency, and physical interpretability—highlighting the complementary strengths of data-driven and physics-guided learning in collider phenomenology.

Modeling dynamical systems faces challenges including data scarcity, high uncertainty, poor interpretability, and unreliable predictions. Method: This paper proposes a novel Physics-Enhanced Machine Learning (PEML) paradigm that unifies conceptual foundations, systematically categorizes approaches into physics-guided, physics-encoded, and physics-constrained methods, and identifies their applicability boundaries and reliability mechanisms. It introduces four types of physics- and domain-knowledge-induced biases to characterize modeling error sources. Methodologically, PEML integrates partial differential equation constraints, conservation law embedding, uncertainty propagation modeling, and interpretability-driven neural architectures. Contribution/Results: Experiments demonstrate that PEML significantly improves accuracy, robustness, and trustworthiness of long-term forecasting and inverse inference under small-data regimes. The framework provides a scientifically grounded yet practically deployable modeling tool for high-consequence engineering decision-making.

To address performance degradation of data-driven control for nonlinear dynamical systems under high-noise measurements, this paper proposes a robust closed-loop control framework integrating physical priors with machine learning. Our method innovatively embeds, for the first time, a control-aware physics-informed neural network (PINN)—i.e., a PINN explicitly incorporating control inputs—into a model predictive control (MPC) architecture, enabling joint noise-robust dynamics modeling and real-time optimal control. We validate the approach on two high-noise nonlinear benchmarks: the Lorenz-3 chaotic system and a turning lathe. Results show a 42% reduction in modeling error and a 3.1× improvement in closed-loop stability over purely data-driven baselines. The core contribution is the development of the first differentiable, MPC-embeddable, control-aware PINN paradigm, which simultaneously ensures physical consistency, noise robustness, and real-time control performance.

This study clarifies the conceptual confusion in physics-oriented machine learning between “interpretability”—referring to model transparency—and “explainability,” which denotes the capacity to map onto domain knowledge. It delineates the boundaries of these two notions and examines their trade-offs in terms of expressive power and adaptability. Through conceptual analysis and the construction of a unifying framework, complemented by a systematic review of both intrinsic and post-hoc explanation methods, the work advocates for integrating interpretability and explainability into scientific modeling paradigms. Crucially, it underscores the central role of task formulation and intervention design in model development. By establishing a clear conceptual foundation and methodological guidance, this research advances the principled integration of machine learning models with scientific reasoning in physics.

This work proposes the VERaiPHY framework to ensure the reliability and scientific rigor of machine learning systems in fundamental physics discovery. It systematically delineates, for the first time, the validation requirements and applicability boundaries of artificial intelligence across particle physics, astrophysics, and cosmology. By integrating statistical inference, hypothesis testing, and machine learning verification methodologies, the framework establishes a reliability assessment paradigm tailored to fundamental physics. It elucidates how inductive biases, sample complexity, and experimental constraints fundamentally limit AI-driven scientific discovery. Furthermore, the study underscores the dual role of physicists—as both domain experts and evaluators—in the design and validation of AI systems, thereby providing a theoretical foundation and practical guidance for the responsible integration of artificial intelligence into scientific discovery processes.

This study addresses the limitations of purely data-driven machine learning in prognostics and health management (PHM)—notably poor generalization, lack of causal reasoning, and limited interpretability—by proposing a systematic literature review that establishes a four-category taxonomy of physics-informed machine learning (PIML): observational bias, inductive bias, learning bias, and hybrid approaches. The framework is evaluated through categorization by PHM tasks across 212 studies. Findings indicate that PIML consistently outperforms conventional methods in applications such as lithium-ion batteries and bearings; however, its adoption remains constrained by narrow application scope, absence of a universal design paradigm, and insufficient empirical validation for certain claimed advantages. This work provides a structured perspective and a research roadmap to advance the systematic development of PIML in PHM.

This study addresses the challenges of applying conventional machine learning to physics-dominated manufacturing processes, where experimental data are scarce, expensive, and highly material-specific. The authors propose an integrated framework that combines physical knowledge with data-driven methods to systematically investigate, under limited-data conditions, the impact of data cleaning, feature selection, physics-informed fusion mechanisms, and evaluation strategies on model performance. They innovatively interpret statistically driven feature selection as an explicit modeling assumption and uncover significant instability in model evaluation under small-sample regimes. Experimental results demonstrate that a Gaussian process augmented with residual learning consistently outperforms other approaches, achieving well-calibrated predictive uncertainty—exhibiting an empirical 86% coverage for a nominal 90% prediction interval. However, while residual learning enhances the stability of Gaussian processes, it adversely affects tree-based models.