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From PINNs to PIKANs: recent advances in physics-informed machine learning

Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements. Over the past few years, significant advancements have been made in the training and optimization of PINNs, covering aspects such as network architectures, adaptive refinement, domain decomposition, and the use of adaptive weights and activation functions. A notable recent development is the Physics-Informed Kolmogorov-Arnold Networks (PIKANS), which leverage a representation model originally proposed by Kolmogorov in 1957, offering a promising alternative to traditional PINNs. In this review, we provide a comprehensive overview of the latest advancements in PINNs, focusing on improvements in network design, feature expansion, optimization techniques, uncertainty quantification, and theoretical insights. We also survey key applications across a range of fields, including biomedicine, fluid and solid mechanics, geophysics, dynamical systems, heat transfer, chemical engineering, and beyond. Lastly, we review computational frameworks and software tools developed by both academia and industry to support PINN research and applications.

Kolmogorov-Arnold networks

Nuclear Safety [Vol. 34, No. 1, January-March 1993]

Nuclear Safety is a review journal that covers significant developments in the field of nuclear safety. Its scope includes the analysis and control of hazards associated with nuclear energy, operations involving fissionable materials, and the products of nuclear fission and their effects on the environment. Primary emphasis is on safety in reactor design, construction, and operation; however, the safety aspects of the entire fuel cycle, including fuel fabrication, spent-fuel processing, nuclear waste disposal, handling of radioisotopes, and environmental effects of these operations, are also treated. Table of Contents for this issue follows. GENERAL SAFETY CONSIDERATIONS: 1 An Integrated Regional Approach To Risk Management of Industrial Systems, S. Chakraborty and R. Stratton; 9 Annual Technical Meeting of the NRC Cooperative Severe Accident Research Program, E. G. Silver; ACCIDENT ANALYSIS: 13 Deterministic Severe Accident Criteria as Severe Accident Design Criteria and Policy for the New Production Reactor-Heavy Water Reactor, P. T. Rhoads; 20 Proposed Deterministic Severe Accident Criteria for the Heavy Water Reactor-New Production Reactor Containment, K. D. Bergeron, S. E. Slezak, and C. E. Leach; 33 Quasi-Static Core Liquid Level Depression and Long-Term Core Uncovery During a PWR LOCA, Y. Kukita, R. R. Schultz, H. Nakamura, and J. Katayama; 49 LIRA: An Advanced Containment System to Minimize the Accidental Radioactivity Releases, A. Turricchia; 63 Errata to “A Review of Hydrogen Production During Melt/Water Interaction in LWRs,” Vol. 33, No. 4; CONTROL AND INSTRUMENTATION: 64 The Nuplex 80+™ Advanced Control Complex from ABB Combustion Engineering, F. Ridolfo, D. Harmon, and K. Scarola; DESIGN FEATURES: 76 A Scheme for Passive Isolation of the Containment of a Reactor, A. K. Ghosh, V. V. Raj, and K. Kakodkar; 84 Utility Requirements for Safety in the Passive Advanced Light-Water Reactor, T. U. Marston, W. H. Layman, and G. Bockhold, Jr.; WASTE AND SPENT FUEL MANAGEMENT: 91 Activities Related to Waste and Spent Fuel Management, Compiled by M. D. Muhlheim and E. G. Silver; OPERATING EXPERIENCES: 103 Testing Deficiencies in Auxiliary Systems Feedwater Systems, J. D. Kueck; 110 Reactor Shutdown Experience, Compiled by J. W. Cletcher; 113 Selected Safety-Related Events, Compiled by G. A. Murphy; 115 Operating U.S. Power Reactors, Compiled by M. D. Muhlheim and E. G. Silver; RECENT DEVELOPMENTS: 133 General Administrative Activities, Compiled by M. D. Muhlheim and E. G. Silver; 145 Reports, Standards, and Safety Guides, D. S. Queener; 150 Proposed Rule Changes as of Sept. 30, 1992; ANNOUNCEMENTS: 75 Harvard Short Course on Risk: Science, Assessment, and Management; 102 International Conference on Reactor Physics and Reactor Computations; 102 The Fourth International Conference on Nuclear Waste Reprocessing and Waste Management [RECOD ’94]; 132 International Symposium on the Radiological Exposure of the Population of the European Community from Radioactivity in the Mediterranean Sea [MARINA-MED]; 162 International High-Level Radioactive Waste Conference ‘Technology Integration—Above and Below”; 154 The Authors; 158 Indexes to Nuclear Safety, Volume 33.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

What is the Quark-Gluon Plasma made of?

This article surveys our present understanding of the internal structure of the fully developed quark-gluon plasma at temperatures outside the crossover region. The theoretical part of the review covers perturbative and nonperturbative approaches to quark-gluon plasma structure, in particular, hard-thermal loop effective theory, lattice QCD and the functional renormalization group. The phenomenological part of the review scrutinizes the information that has been derived from bulk observables and hard probes in relativistic heavy ion collisions in terms of how it informs our knowledge about the structure of the quark-gluon plasma. The final section lists possible avenues for future progress.

FOS: Physical sciences

Small Co-doping induced magnetic and electrical transitions in single crystal CaF⁢e 0.95 ⁢C⁢o 0.05 ⁢O 3

CaFe⁢O 3 and CaF⁢e 0.95 ⁢C⁢o 0.05 ⁢O 3 single crystals were grown by combing floating-zone method with high oxygen pressure treatment. Both crystals show charge disproportionation of Fe (F⁡e 4+ → F⁡e 3+ + F⁡e 5+ ) accompanied by a metal-to-insulator transition as well as a crystal structural transformation from Pbnm to 𝑃⁢2 1 /𝑛. However, the slight introduction of Co significantly suppresses the critical temperature of charge disproportionation from 290 K in CaFe⁢O 3 to 260 K in CaF⁢e 0.95 ⁢C⁢o 0.05 ⁢O 3 . Different from the single antiferromagnetic phase transition as observed in the polycrystalline CaFe⁢O 3 , two sequential antiferromagnetic transitions are found to occur in these two single crystals with the Néel temperatures around 119 and 112 K for CaFe⁢O 3 crystal and 109 and 98 K for CaF⁢e 0.95 ⁢C⁢o 0.05 ⁢O 3 crystal, respectively. Neutron diffraction illustrates the formation of a spiral antiferromagnetic structure. Moreover, as the temperature further decreases to 65 K, a third magnetic transition accompanied by a second electrical transition is observed in the slightly Co-doped CaF⁢e 0.95 ⁢C⁢o 0.05 ⁢O 3 crystal. In conclusion, first-principles calculations suggest that the introduction of a moderate amount of Co and the peculiar spiral spin texture play an important role in the presence of such new magnetic and electrical transitions.

Xia, Hailiang [Chinese Academy of Sciences (CAS),

Feedback, physics, and forecasts: The emerging paradigm of machine learning-driven battery research

Machine learning (ML) is reshaping how we understand, predict, and optimize electrochemical systems. In batteries, ML accelerates discovery across chemistry, design, and operation by transforming massive experimental and simulated datasets into predictive, interpretable models. This review consolidates a decade of progress in ML-driven battery innovation, from early-cycle feature extraction to operando image analysis and physics-informed modeling. We categorize approaches by data domain and physical fidelity, emphasizing interpretable ML for diagnostics, reinforcement learning for control, and multi-objective optimization for lifetime extension strategies. Additionally, we demonstrate how integrated models accelerate discovery, reduce testing time, and guide sustainable design. Economic analyses furthermore illustrate how these advances can lower cost per cycle and improve circularity. Together, these developments chart a path toward self-optimizing, sustainable battery technologies.

artificial intelligence

Statistical Study of Energy Dissipation in Magnetic Structures During Turbulent Reconnection in the Earth's Magnetotail

Magnetic reconnection is a ubiquitous plasma phenomenon that plays a critical role in particle heating and energization. During reconnection, the topology of magnetic field rearranges, depositing energy into the surrounding plasma through bulk flow, thermal heating, or non-thermal particle acceleration. While the pathways of this transformation from magnetic energy into kinetic have been studied extensively in recent years through theoretical or case-by-case observations, comprehensive statistical studies remain limited. In this paper, we present a statistical investigation using data from the Magnetospheric Multiscale (MMS) mission, and detail the particle energization mechanisms in magnetic structures found near reconnecting regions in turbulent Earth's magnetotail. We find that electrons with motion perpendicular to the magnetic field dominate $\vec{j}$ ⋅ $\vec{E}$ dissipation. In contrast to the conventional picture of unidirectional energy transfer to particles by laminar two-dimensional (2D) reconnection, we find that energy exchange within magnetic structures during turbulent reconnection tends to be bidirectional with only a small positive bias from electromagnetic fields to particles. Specific electron energization mechanisms are quantified, including those due to parallel electric field, Fermi energization from curvature drift, betatron heating from magnetic field inhomogeneity, and polarization drift.

Wang, Rachel [Princeton University, NJ (United Sta

Role of ion acoustic instability in magnetic reconnection

We report on a first-principles numerical study of magnetic reconnection in plasmas with different initial ion-to-electron temperature ratios. In cases where this ratio is significantly below unity, we observe intense wave activity in the diffusion region, driven by the ion-acoustic instability. Our analysis shows that the dominant macroscopic effect of this instability is to drive substantial ion heating. In contrast to earlier studies reporting significant anomalous resistivity, we find that anomalous contributions due to the ion-acoustic instability are minimal. These results shed light on the dynamical impact of this instability on reconnection processes, offering new insights into the fundamental physics governing collisionless reconnection.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Theory of the thermionic current beyond the traditional space charge limit enabled by trapped ions in the virtual cathode

We show that trapped ions in virtual cathode potential wells can raise the transmitted current of emitted electrons into a plasma much closer to the full emission than is predicted by cathode sheath theories without trapped ions. The transmitted current is controlled by the well barrier voltage, which must adjust to balance the creation of low-energy ions within the well, and their loss. Our model considers the case of a plasma-facing cathode where trapped ions are created passively via charge-exchange collisions and lost passively via thermal leakage over the well. We quantify these rates and estimate the current in terms of system parameters for thermionic emission into a plasma with several cathode geometries. A general prediction is that the current as a function of emitted flux does not saturate at the traditional space charge limit (the onset of a well) but can reach far higher values until the trapped ion balance breaks down, causing instability. The maximum stable current depends on parameters but in principle can be arbitrarily high if active techniques are used to manipulate the trapped ion balance. We conclude that major improvements in plasma technologies with hot cathodes might be achieved by optimizing the current enhancement enabled by trapped ions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Autonomous phototaxis of hydrogel swimmers

The design of synthetic soft matter capable of emulating the complex behaviors of living organisms, such as sensing and adapting to their environment, remains an important challenge in developing biomimetic materials. Functionalized hydrogels are ideal candidates for such materials since they are highly responsive to their environment and can be operated in water. In this work, we investigate a hybrid bonding hydrogel composed of peptide amphiphile supramolecular nanofibers covalently attached to a photoresponsive network, in which high-aspect-ratio ferromagnetic nanowires are aligned along the length of the sample, designed to swim under oscillating magnetic fields. This hybrid hydrogel swimmer can autonomously swim toward a light source by utilizing photoinduced interactions between supramolecular and covalent networks reminiscent of phototactic swimming in living systems. Using a combination of experimental techniques and a continuum model incorporating photochemistry, magnetoelasticity, and hydrodynamics, we explain the swimming mechanism and predict phototactic behavior. Our work highlights the potential role of hybrid bonding polymers, which leverage the interplay between supramolecular assemblies and covalent networks. We demonstrate how these polymers can be tailored to react dynamically to their environment, paving the way for developing intelligent and autonomous robotic systems.

Science & Technology - Other Topics

Recent Progress in the Electroweak Structure of Light Nuclei Using Quantum Monte Carlo Methods

Nuclei will play a prominent role in searches for physics beyond the Standard Model as the active material in experiments. In order to reliably interpret new physics signals, one needs an accurate model of the underlying nuclear dynamics. In this review, we discuss recent progress made with quantum Monte Carlo approaches for calculating the electroweak structure of light nuclei. We place particular emphasis on recent β decay, muon capture, neutrinoless double β decay, and electron scattering results.

Physics