{"title":"Structure functions and intermittency for coarsening systems.","authors":"Pradeep Kumar Yadav, Mahendra Kumar Verma, Sanjay Puri","doi":"10.1098/rsta.2025.0025","DOIUrl":"https://doi.org/10.1098/rsta.2025.0025","url":null,"abstract":"<p><p>In studies of turbulence, there has been extensive use of physical quantities such as energy transfers and structure functions. We examine whether these quantities can be useful in understanding problems of domain growth or coarsening, as modelled by the time-dependent Ginzburg-Landau (TDGL) equation and the Cahn-Hilliard (CH) equation. This paper has two major themes. First, we review our recent papers on energy transfers in domain growth. Second, we study structure functions and intermittency for coarsening systems. As a consequence of sharp interfaces, the structure functions scale as Sq∼rζq, where r is the distance between two points. For the TDGL and CH models, ζq=1, indicating anomalous scaling. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2325","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148631407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sayak Bhattacharjee, Mahendra K Verma, Alexander V Balatsky, Srinivas Raghu
{"title":"Quantum turbulence in the many-body regime.","authors":"Sayak Bhattacharjee, Mahendra K Verma, Alexander V Balatsky, Srinivas Raghu","doi":"10.1098/rsta.2025.0018","DOIUrl":"https://doi.org/10.1098/rsta.2025.0018","url":null,"abstract":"<p><p>We discuss phenomenology associated with turbulent hydrodynamics in quantum fluids from a condensed-matter perspective. We begin with weakly interacting superfluids, often modelled by a mean-field theory governed by the Gross-Pitaevskii (GP) equation. Considering the effect of quantum fluctuations beyond the mean-field approximation, we propose a study of many-body quantum effects in turbulent hydrodynamics, especially near zero temperature. We indicate examples of quantum many-body systems where such effects may be uncovered. These include bosons confined in a periodic potential in low spatial dimensions (one and two), and the associated quantum critical point of the superfluid-insulator transition, realized in present-day ultracold-atom and quantum computing platforms. We conclude by listing a set of (open) questions that may be answered using modern quantum many-body techniques. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2325","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148631292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Erika Paola Ortiz Bernal, Ciro S Campolina, Alexei A Mailybaev
{"title":"Spontaneous stochasticity in the fluctuating Navier-Stokes equations on a logarithmic lattice.","authors":"Erika Paola Ortiz Bernal, Ciro S Campolina, Alexei A Mailybaev","doi":"10.1098/rsta.2025.0031","DOIUrl":"https://doi.org/10.1098/rsta.2025.0031","url":null,"abstract":"<p><p>The predictability of turbulent flows remains a challenging problem for mathematicians, physicists and meteorologists. In this context, we consider the three-dimensional incompressible Navier-Stokes equations with small-scale random forcing on logarithmic lattices in Fourier space. Our goal is to probe the phenomenon of spontaneous stochasticity in this system, which means that its solutions remain stochastic in the limit of vanishing viscosity and noise. For this, we consider numerical simulations with increasing Reynolds numbers and vanishing noise amplitudes. Through measurements of statistics of individual large-scale Fourier modes, we verify the spontaneous stochasticity in two different setups: from rough initial data, and after a finite-time blowup of a strong solution. The convergence of probability density functions for distinct parameters suggests that the limiting solution is a universal stochastic process. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2325","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148631466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alexander Bastounis, Desmond J Higham, Ivan Tyukin
{"title":"A survey of inevitability results in AI instability.","authors":"Alexander Bastounis, Desmond J Higham, Ivan Tyukin","doi":"10.1098/rsta.2025.0128","DOIUrl":"https://doi.org/10.1098/rsta.2025.0128","url":null,"abstract":"<p><p>Over the past decade, there has been an explosion of activity in the design of algorithms for adversarially attacking artificial intelligence (AI) systems; especially in the context of image classification. For example, a carefully crafted perturbation to an image that is imperceptible to the human eye may cause a sophisticated convolutional neural network to change its classification. To deal with this vulnerability, algorithms that detect or defend against such attacks have also been proposed. It has been observed empirically that attackers have the upper hand. To explain these observations, various theoretical results have subsequently emerged. This article will review some recent rigorous results, emphasizing what assumptions they use, in terms of (i) the nature of the training data, (ii) the network architectures, and (iii) the information available to the attacker. We also discuss how the results may give guidelines for building more secure systems, and how this research area can inform the design of AI regulations. This article is part of the theme issue 'Safe, secure and robust AI for safety-critical systems'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2324","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148472128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thomas Baldwin-McDonald, Amir Fard, David Fletcher, Andreas Gutmann, Qiqi Su
{"title":"Online safety by design: towards user-centric development of safer AI-based systems.","authors":"Thomas Baldwin-McDonald, Amir Fard, David Fletcher, Andreas Gutmann, Qiqi Su","doi":"10.1098/rsta.2025.0126","DOIUrl":"10.1098/rsta.2025.0126","url":null,"abstract":"<p><p>In this opinion piece, we present the view that the safety and security of end users should be placed at the heart of the design and development of any AI-based system deployed on an online service to ensure that risks of harm are minimized. We also posit that while well-crafted regulatory frameworks are necessary to ensure user safety, the growing awareness among users of issues related to trust and safety creates an additional incentive for providers of online services to prioritize user well-being. We provide a brief overview of how online safety relates to several widely used systems on online services that utilize or interact with AI, discussing examples of potential risks of harm, which may be enabled or reinforced by these systems, alongside techniques for mitigating these harms. Future challenges and opportunities across these areas are discussed, along with a summary of how user, device and platform diversity can impact users' experiences with AI-based systems on online services. This article is part of the theme issue 'Safe, secure and robust AI for safety-critical systems'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2324","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148472088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Implicit regularization makes overparameterized asymmetric matrix sensing robust to perturbations.","authors":"Johan Sokrates Wind","doi":"10.1098/rsta.2025.0120","DOIUrl":"https://doi.org/10.1098/rsta.2025.0120","url":null,"abstract":"<p><p>Several key questions remain unanswered regarding overparameterized learning models. It is unclear how (stochastic) gradient descent finds solutions that generalize well, and in particular the role of small random initializations. Matrix sensing, which is the problem of reconstructing a low-rank matrix from a few linear measurements, has become a standard prototypical setting to study these phenomena. Previous works have shown that matrix sensing can be solved by factorized gradient descent, provided the random initialization is extremely small. In this paper, we find that factorized gradient descent is highly robust to certain perturbations. This lets us use a perturbation term to capture both the effects of imperfect measurements, discretization by gradient descent, and other noise, resulting in a general formulation which we call perturbed gradient flow. We find that not only is this equivalent formulation easier to work with, but it leads to sharper sample and time complexities than previous work, handles moderately small initializations, and the results are naturally robust to perturbations such as noisy measurements or changing measurement matrices. Finally, we also analyse mini-batch stochastic gradient descent using the formulation, where we find improved sample complexity. This article is part of the theme issue 'Safe, secure and robust AI for safety-critical systems'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2324","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148472057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Limitations of public chest radiography datasets for artificial intelligence: label quality, domain shift, bias and evaluation challenges.","authors":"Amy Rafferty, Ajitha Rajan","doi":"10.1098/rsta.2025.0129","DOIUrl":"https://doi.org/10.1098/rsta.2025.0129","url":null,"abstract":"<p><p>Artificial intelligence (AI) has shown significant promise in chest radiography, where deep learning models can approach radiologist-level diagnostic performance. Progress has been accelerated by large public datasets, such as MIMIC-CXR, ChestX-ray14, PadChest and CheXpert, which provide hundreds of thousands of labelled images with pathology annotations. However, these datasets also present important limitations. Automated label extraction from radiology reports introduces errors, particularly in handling uncertainty and negation, and radiologist review frequently disagrees with assigned labels. In addition, domain shift and population bias restrict model generalizability, while evaluation practices often overlook clinically meaningful measures. We conduct a systematic analysis of these challenges, focusing on label quality, dataset bias and domain shift. Our cross-dataset domain-shift evaluation across multiple model architectures revealed substantial external performance degradation, with pronounced reductions in area under the precision-recall curve (AUPRC) and F1 scores compared with internal testing. To assess dataset bias, we trained a source-classification model that distinguished datasets with near-perfect accuracy, and performed subgroup analyses showing reduced performance for minority age and sex groups. Finally, expert review by two board-certified radiologists identified significant disagreement with public dataset labels. Our findings highlight important clinical weaknesses in current benchmarks and emphasize the need for clinician-validated datasets and fairer evaluation frameworks. This article is part of the theme issue 'Safe, secure and robust AI for safety-critical systems'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2324","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148472067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Is it safe to deploy AI in safety-critical systems?","authors":"Tamara G Kolda","doi":"10.1098/rsta.2025.0123","DOIUrl":"https://doi.org/10.1098/rsta.2025.0123","url":null,"abstract":"<p><p>We consider the reality of deploying artificial intelligence (AI) in safety-critical systems, such as autonomous vehicles, medical diagnoses and weather forecasting. Our discussion is grounded in the mathematical nature of AI systems, including how an AI's mathematical properties relate to its benefit and risk profile. Benefits include the ability to learn models from data even when no physical model exists, increased automation and enhanced speed compared with traditional approaches. Risks of AI include its opaque (mis-)understanding of the world, failures on out-of-distribution inputs, its insatiable appetite for data and computation and the ongoing challenge of aligning the AI's objectives with human values. Such risks are potentially manageable with clear-eyed expectations, and our hope in this work is to clarify what can be expected. This article is part of the theme issue 'Safe, secure and robust AI for safety-critical systems'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2324","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148472101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the next generation for neuromorphic computing and neuromorphic AI.","authors":"Peter Grindrod","doi":"10.1098/rsta.2025.0122","DOIUrl":"10.1098/rsta.2025.0122","url":null,"abstract":"<p><p>As we learn more about the inner cognitive workings of the brain's information processing and decision-making behaviours, this naturally leads us to consider alternative and additional ways to process information, from chips and architectures through the generation of insights and decisions. In turn, this suggests some options that might respond to challenges that are not addressable by the present state-of-the-art. By their nature, however, they may develop some common features and idiosyncrasies that are associated with human cognition, such as individual expertise and blind spots, illusions, systematic errors and transient mindsets, as well as evolutionarily advantageous fast-thinking facilities, which are applicable within novel and data-poor circumstances. We discuss some of the lessons learned from the reverse engineering of very large-scale neuron-to-neuron simulations (1B neurons) within cortex-like, network-of-networks, architectures. We identify some elements of the dynamical behaviour of the inner sub-networks (neural columns) that are not exhibited by present-day neuromorphic chips, owing to conceptual and design limitations. We describe a novel mathematical framework that might encompass human cognitive processing alongside various future neuromorphic processing concepts. We also identify certain elements of human cognition, reasoning and performance that present-day chips and present-day artificial intelligence (AI) simply cannot fully emulate (match to a high standard, in some artificial way), or simulate (achieve in the same way). We discuss how these aspects might catalyse some new fields of development for both processors and AI methodologies. In short, we discuss how future research and development will respond in radical ways that are precluded by most present-day technologies. This article is part of the theme issue 'Safe, secure and robust AI for safety-critical systems'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2324","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148472046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mitigating medical bias in large language models by prompt engineering: an empirical study of effectiveness and trade-offs.","authors":"Ying Xiao, Zhenpeng Chen, Jie Zhang","doi":"10.1098/rsta.2025.0125","DOIUrl":"https://doi.org/10.1098/rsta.2025.0125","url":null,"abstract":"<p><p>Large language models (LLMs) demonstrate expert-level performance in various medical scenarios, yet their outputs can exhibit bias against groups or individuals with specific sensitive attributes, posing risks to patient safety and undermining trust in LLMs for healthcare. Recent research suggests that prompt engineering offers a convenient way to adjust model outputs, with the potential to mitigate such biases. However, there is a lack of empirical studies that systematically examine the effectiveness of prompt engineering and its trade-offs among fairness, accuracy and inference overhead. To fill this gap, we empirically evaluate five widely used prompting strategies across five influential LLMs in the latest medical bias benchmark. Results reveal substantial heterogeneity in both effectiveness and overhead across models, with no strategy proving universally effective and some even exacerbating bias. Chain-of-thought prompting yields the largest reduction, lowering the average gap across all scenarios by 2.4 percentage points, where the largest reduction is 6.2 percentage points, obtained in the DeepSeek-V3.1-sex case. Furthermore, the results of the McNemar test also show that it achieves the largest number of significant bias reduction cases (8/15), primarily by improving performance on unprivileged groups. These findings provide practical guidance for the fair deployment of LLMs in healthcare and highlight that mitigating medical bias remains a challenging problem requiring sustained efforts from both the artificial intelligence (AI) and medical communities. To support future research on fair AI in healthcare, we shall release all results and source code. This article is part of the theme issue 'Safe, secure and robust AI for safety-critical systems'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"384 2324","pages":""},"PeriodicalIF":3.7,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148472134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}