Physical Systems Research Articles

Decomposing causality into its synergistic, unique, and redundant components

Causality lies at the heart of scientific inquiry, serving as the fundamental basis for understanding interactions among variables in physical systems. Despite its central role, current methods for causal inference face significant challenges due to nonlinear dependencies, stochastic interactions, self-causation, collider effects, and influences from exogenous factors, among others. While existing methods can effectively address some of these challenges, no single approach has successfully integrated all these aspects. Here, we address these challenges with SURD: Synergistic-Unique-Redundant Decomposition of causality. SURD quantifies causality as the increments of redundant, unique, and synergistic information gained about future events from past observations. The formulation is non-intrusive and applicable to both computational and experimental investigations, even when samples are scarce. We benchmark SURD in scenarios that pose significant challenges for causal inference and demonstrate that it offers a more reliable quantification of causality compared to previous methods.

Quantifying the reciprocal impacts of capital and logistics networks in the supply chains: A cyber–physical system approach

Capital flow and logistics are closely linked in the supply chain. Current research primarily assesses their independent resilience during disruptions, but this study reveals an iterative bidirectional impact. The interconnection of shareholding, mutual guarantees, and borrowing within the supply chain has created financial relationships that were previously nonexistent. However, the evolution of logistics has not aligned with these financial developments, leading to a growing heterogeneity between capital flow and logistics. While the heterogeneity between capital flow and logistics within supply chains is crucial, previous studies, especially those rooted in complex networks, often overlook its impact. Drawing inspiration from the cyber–physical system, this paper abstracts logistics and capital flow into respective networks. A model of mutual dependence quantifies reciprocal impacts between capital and logistics networks, exploring the consequences of heterogeneity on the supply chain. Simulation results are compared with traditional single-layer network models. Finally, an innovative edge removal method is proposed to enhance supply chain robustness. Our simulation results indicate that the influence of the capital network on the logistics network and their relationship to heterogeneity is nonlinear. The edge removal method enhances supply chain network robustness in a nonlinear manner, with optimal effectiveness achieved at p_l=0.2.

Propagation Speeds of Relativistic Conformal Particles from a Generalized Relaxation Time Approximation

The propagation speeds of excitations are a crucial input in the modeling of interacting systems of particles. In this paper, we assume the microscopic physics is described by a kinetic theory for massless particles, which is approximated by a generalized relaxation time approximation (RTA) where the relaxation time depends on the energy of the particles involved. We seek a solution of the kinetic equation by assuming a parameterized one-particle distribution function (1-pdf) which generalizes the Chapman–Enskog (Ch-En) solution to the RTA. If developed to all orders, this would yield an asymptotic solution to the kinetic equation; we restrict ourselves to an approximate solution by truncating the Ch-En series to the second order. Our generalized Ch-En solution contains undetermined space-time-dependent parameters, and we derive a set of dynamical equations for them by applying the moments method. We check that these dynamical equations lead to energy–momentum conservation and positive entropy production. Finally, we compute the propagation speeds for fluctuations away from equilibrium from the linearized form of the dynamical equations. Considering relaxation times of the form τ=τ0(−βμpμ)−a, with −∞<a<2, where βμ=uμ/T is the temperature vector in the Landau frame, we show that the Anderson–Witting prescription a=1 yields the fastest speed in all scalar, vector and tensor sectors. This fact ought to be taken into consideration when choosing the best macroscopic description for a given physical system.

Full-field expansion and damage detection from sparse measurements using physics-informed variational autoencoders

Recent advancements in machine learning and artificial neural network algorithms have created new opportunities for expanding sparse measurements to full-field representations. However, these methods often face accuracy challenges when used for condition monitoring of physical systems. For example, traditional autoencoders can capture complex phenomena and their underlying physics in the latent space, but due to their frequentist nature, they lack generative and damage detection capabilities. To address these challenges, a novel physics-informed variational autoencoder (PI-VAE) network is proposed for expanding sparse measurements to full-field representations while also detecting damage. The effectiveness of the proposed PI-VAE network is evaluated through analytical and experimental studies on a metal plate under thermal excitation with embedded defects of various sizes and types. In the analytical studies using finite-element model data, the PI-VAE accurately expanded full-field temperature distributions and identified the dimensions of cracks, spalling, and hole-like defects with errors smaller than 5%. When tested with experimental data, the PI-VAE network maintained robust performance, detecting damage with errors smaller than 6%, despite being trained on undamaged data only. These findings demonstrate the PI-VAE’s potential as a reliable tool for full-field expansion and damage detection in structural health monitoring and nondestructive evaluation, even when limited sensors and datasets are available.

Multi-agent Deep Reinforcement Learning for cloud-based digital twins in power grid management

As the power industry becomes increasingly complex, Digital Twin (DT) technology has emerged as a crucial tool for enhancing grid resilience and operational efficiency by creating dynamic digital replicas of physical systems. These replicas enable accurate simulations and proactive management, but the vast amount of data generated by DT systems poses significant challenges for processing and analysis. Cloud computing offers a flexible solution by offloading these computational tasks to distributed resources, allowing for real-time analysis and scalable operations. However, this approach introduces complexities in task distribution and maintaining quality of service. Recent efforts have applied Deep Reinforcement Learning (DRL) to address these challenges, primarily using single-agent methods. However, these methods struggle with scalability and performance in increasingly complex cloud environments. To overcome these limitations, we propose an efficient task scheduling framework based on Multi-Agent Deep Q-Network (MADQN) principles, specifically designed to optimize both response times and operational costs. We provide a comprehensive design overview of our approach and conduct a thorough evaluation of its performance. The experimental results clearly indicate that our approach can considerably reduce response times amd lower operational costs compared to current methods, including state-of-the-art single-agent approaches.

An Adaptive Energy Orchestrator for Cyberphysical Systems Using Multiagent Reinforcement Learning

Reducing carbon emissions is a critical issue for the near future as climate change is an imminent reality. To reduce our carbon footprint, society must change its habits and behaviours to optimise energy consumption, and the current progress in embedded systems and artificial intelligence has the potential to make this easier. The smart building concept and intelligent energy management are key points to increase the use of renewable sources of energy as opposed to fossil fuels. In addition, cyber-physical systems (CPSs) provide an abstraction of the management of services that allows the integration of both virtual and physical systems in a seamless control architecture. In this paper, we propose to use multiagent reinforcement learning (MARL) to model the CPS services control plane in a smart house, with the purpose of minimising, by shifting or shutdown services, the use of non-renewable energy (fuel generator) by exploiting solar production and batteries. Furthermore, our proposal dynamically adapts its behaviour in real time according to current and historic energy production, thus being able to handle occasional changes in energy production due to meteorological phenomena or unexpected energy consumption. In order to evaluate our proposal, we have developed an open-source smart building energy simulator and deployed our use case. Finally, several simulations with different configurations are evaluated to verify the performance. The simulation results show that the reinforcement learning solution outperformed the priority-based and the heuristic-based solutions in both power consumption and adaptability in all configurations.

Geospatial tools and data for health service delivery: opportunities and challenges across the disaster management cycle.

As extreme weather events increase in frequency and intensity, the health system faces significant challenges, not only from shifting patterns of climate-sensitive diseases but also from disruptions to healthcare infrastructure, supply chains and the physical systems essential for delivering care. This necessitates the strategic use of geospatial tools to guide the delivery of healthcare services and make evidence-informed priorities, especially in contexts with scarce human and financial resources. In this article, we highlight several published papers that have been used throughout the phases of the disaster management cycle in relation to health service delivery. We complement the findings from these publications with a rapid scoping review to present the body of knowledge for using spatial methods for health service delivery in the context of disasters. The main aim of this article is to demonstrate the benefits and discuss the challenges associated with the use of geospatial methods throughout the disaster management cycle. Our scoping review identified 48 articles employing geospatial techniques in the disaster management cycle. Most of them focused on geospatial tools employed for preparedness, anticipatory action and mitigation, particularly for targeted health service delivery. We note that while geospatial data analytics are effectively deployed throughout the different phases of disaster management, important challenges remain, such as ensuring timely availability of geospatial data during disasters, developing standardized and structured data formats, securing pre-disaster data for disaster preparedness, addressing gaps in health incidence data, reducing underreporting of cases and overcoming limitations in spatial and temporal coverage and granularity. Overall, existing and novel geospatial methods can bridge specific evidence gaps in all phases of the disaster management cycle. Improvement and 'operationalization' of these methods can provide opportunities for more evidence-informed decision making in responding to health crises during climate change.

Shielded Reinforcement Learning for Safe and Optimal Cyber Physical Systems

Shielded Reinforcement Learning for Safe and Optimal Cyber Physical Systems

The Application of Information Theory to Interpret Shore Platform Erosion Rates

Advancements in information physics have recently introduced the application of information theory to investigate physical systems. The behaviour of erosion at the granular scale is to date still a complex system to unpack, and therefore geomorphology research requires novel approaches to better inform the interpretation of temporal and spatial erosion patterns at different scales. This paper applies information theory concepts to re-evaluate erosional data that were measured on limestone surfaces of two shore platforms in Malta with a traversing micro-erosion meter (TMEM). By representing erosion rates through their information content using a Box-Cox style transformation of the raw data (application of an inverse normal distribution function to fractionally ranked data), it is possible to identify points and measurement periods that contribute to a disproportionately large share of unexpected erosion rates that could provide more insight into the causes of erosion rates. Despite the variations in the information content from erosion rates at individual measurement points, most points consistently contribute to a similar amount of information. These findings illuminate the importance of considering the informational value of erosion data to further understand the underlying physical processes and potentially improve predictive models.

Characterizing southeast Greenland fjord surface ice and freshwater flux to support biological applications

Abstract. Southeast Greenland (SEG) is characterized by complex morphology and environmental processes that create dynamic habitats for top marine predators. Active glaciers producing solid-ice discharge, freshwater flux, offshore sea ice transport, and seasonal landfast-ice formation all contribute to a variable, transient environment within SEG fjord systems. Here, we investigate a selection of physical processes in SEG to provide a regional characterization that reveals physical system processes and supports biological research. SEG fjords exhibit high fjord-to-fjord variability regarding bathymetry, size, shape, and glacial setting, influencing some processes more than others. For example, during fall, the timing of offshore sea ice formation near SEG fjords progresses temporally when moving southward across latitudes, while the timing of offshore sea ice disappearance is less dependent on latitude. The rates of annual freshwater flux into fjords, however, are highly variable across SEG, with annual average input values ranging from ∼ 1 × 108 to ∼ 1.25 × 1010 m3 (∼ 0.1–12.5 Gt) for individual fjords. Similarly, the rates of solid-ice discharge in SEG fjords vary widely – partly due to the irregular distribution of active glaciers across the study area (60–70° N). Landfast sea ice, assessed for eight focus fjords, is seasonal and has a spatial distribution highly dependent on individual fjord topography. Conversely, glacial ice is deposited into fjord systems year-round, with the spatial distribution of glacier-derived ice depending on the location of glacier termini. As climate change continues to affect SEG, the evolution of these metrics will vary individually in their response, and next steps should include moving from characterization to system projection. Due to the projected regional ice sheet persistence that will continue to feed glacial ice into fjords, it is possible that SEG could remain a long-term refugium for polar bears and other ice-dependent species on a centennial to millennial scale, demonstrating a need for continued research into the SEG physical environment.

Is stochastic thermodynamics the key to understanding the energy costs of computation?

The relationship between the thermodynamic and computational properties of physical systems has been a major theoretical interest since at least the 19th century. It has also become of increasing practical importance over the last half-century as the energetic cost of digital devices has exploded. Importantly, real-world computers obey multiple physical constraints on how they work, which affects their thermodynamic properties. Moreover, many of these constraints apply to both naturally occurring computers, like brains or Eukaryotic cells, and digital systems. Most obviously, all such systems must finish their computation quickly, using as few degrees of freedom as possible. This means that they operate far from thermal equilibrium. Furthermore, many computers, both digital and biological, are modular, hierarchical systems with strong constraints on the connectivity among their subsystems. Yet another example is that to simplify their design, digital computers are required to be periodic processes governed by a global clock. None of these constraints were considered in 20th-century analyses of the thermodynamics of computation. The new field of stochastic thermodynamics provides formal tools for analyzing systems subject to all of these constraints. We argue here that these tools may help us understand at a far deeper level just how the fundamental thermodynamic properties of physical systems are related to the computation they perform.

Distributed intelligence in industrial and automotive cyber–physical systems: a review

Cyber–physical systems (CPSs) are evolving from individual systems to collectives of systems that collaborate to achieve highly complex goals, realizing a cyber–physical system of systems (CPSoSs) approach. They are heterogeneous systems comprising various autonomous CPSs, each with unique performance capabilities, priorities, and pursued goals. In practice, there are significant challenges in the applicability and usability of CPSoSs that need to be addressed. The decentralization of CPSoSs assigns tasks to individual CPSs within the system of systems. All CPSs should harmonically pursue system-based achievements and collaborate to make system-of-system-based decisions and implement the CPSoS functionality. The automotive domain is transitioning to the system of systems approach, aiming to provide a series of emergent functionalities like traffic management, collaborative car fleet management, or large-scale automotive adaptation to the physical environment, thus providing significant environmental benefits and achieving significant societal impact. Similarly, large infrastructure domains are evolving into global, highly integrated cyber–physical systems of systems, covering all parts of the value chain. This survey provides a comprehensive review of current best practices in connected cyber–physical systems and investigates a dual-layer architecture entailing perception and behavioral components. The presented perception layer entails object detection, cooperative scene analysis, cooperative localization and path planning, and human-centric perception. The behavioral layer focuses on human-in-the-loop (HITL)-centric decision making and control, where the output of the perception layer assists the human operator in making decisions while monitoring the operator’s state. Finally, an extended overview of digital twin (DT) paradigms is provided so as to simulate, realize, and optimize large-scale CPSoS ecosystems.

Research on the Possibilities of Expanding the Photovoltaic Installation in the Microgrid Structure of Kielce University of Technology Using Digital Twin Technology

Global challenges related to sustainable development are increasingly focusing on the use of digital twin technology as a universal tool for optimizing and monitoring renewable energy installations. This article discusses digital twin technology as a support for sustainable development based on the analysis of microgrid structures. Digital twins allow the creation of virtual models of physical systems. This capability facilitated the accurate replication of the microgrid model at Kielce University of Technology using ETAP (Electrical Transient Analyzer Program) software (version 22.5). The operational parameters of the microgrid structure were analyzed for the examined power range of the photovoltaic installation to determine the possibilities of expanding the existing installation. The impact of the photovoltaic installation’s power on the operational parameters of the microgrid structure was visualized, and final conclusions were formulated. Moreover, the integration of digital twin technology into renewable energy systems not only enhances operational efficiency but also plays a pivotal role in advancing sustainability objectives. Through real-time monitoring and predictive maintenance, digital twin technology facilitates the optimization of energy production and distribution, thereby reducing waste and contributing to the overall sustainability of energy systems. This technology enables the simulation of various scenarios, such as fluctuations in energy demand or the integration of new renewable sources, which can inform more sustainable decision-making processes. In the context of microgrids, digital twin technology ensures that energy production is closely aligned with consumption patterns, minimizing energy losses and enhancing grid resilience. Furthermore, digital twin technology supports the sustainable expansion of renewable installations by providing detailed insights into potential environmental impacts and the long-term sustainability of various energy configurations. As the demand for clean energy continues to grow, digital twin technology will be indispensable in achieving a balance between energy needs and environmental stewardship, ensuring that the expansion of renewable energy sources contributes positively to global sustainability objectives.

Synergy as the Failure of Distributivity

The concept of emergence, or synergy in its simplest form, is widely used but lacks a rigorous definition. Our work connects information and set theory to uncover the mathematical nature of synergy as the failure of distributivity. For the trivial case of discrete random variables, we explore whether and how it is possible to get more information out of lesser parts. The approach is inspired by the role of set theory as the fundamental description of part–whole relations. If taken unaltered, synergistic behavior is forbidden by the set-theoretic axioms. However, random variables are not a perfect analogy of sets: we formalize the distinction, highlighting a single broken axiom—union/intersection distributivity. Nevertheless, it remains possible to describe information using Venn-type diagrams. The proposed multivariate theory resolves the persistent self-contradiction of partial information decomposition and reinstates it as a primary route toward a rigorous definition of emergence. Our results suggest that non-distributive variants of set theory may be used to describe emergent physical systems.

Tuning collective behaviour in zebrafish with genetic modification.

Zebrafish collective behaviour is widely used to assess their physical and mental state, serving as a valuable tool to assess the impact of ageing, disease genetics, and the effect of drugs. The essence of these macroscopic phenomena can be represented by active matter models, where the individuals are abstracted as interactive self-propelling agents. The behaviour of these agents depends on a set of parameters in a manner reminiscent of those between the constituents of physical systems. In a few cases, the system may be controlled at the level of the individual constituents such as the interactions between colloidal particles, or the enzymatic behaviour of de novo proteins. Usually, however, while the collective behaviour may be influenced by environmental factors, it typically cannot be changed at will. Here, we challenge this scenario in a biological context by genetically modifying zebrafish. We thus demonstrate the potential of genetic modification in the context of controlling the collective behaviour of biological active matter systems at the level of the constituents, rather than externally. In particular, we probe the effect of the lack of col11a2 gene in zebrafish, which causes the early onset of osteoarthritis. The resulting col11a2 -/- zebrafish exhibited compromised vertebral column properties, bent their body less while swimming, and took longer to change their orientations. Surprisingly, a group of 25 mutant fish exhibited more orderly collective motion than the wildtype. We show that the collective behaviour of wildtype and col11a2 -/- zebrafish are captured with a simple active matter model, in which the mutant fish are modelled by self-propelling agents with a higher orientational noise on average. In this way, we demonstrate the possibility of tuning a biological system, changing the state space it occupies when interpreted with a simple active matter model.

Bloch classification surface for three-band systems

Abstract Topologically protected states can be found in physical systems, that show singularities in some energy contour diagram. These singularities can be characterized by winding numbers, defined on a classification surface, which maps physical state parameters. We have found a classification surface, which applies for three-band hamiltonian systems in the same way than standard Bloch surface does for two-band ones. This generalized Bloch surface is universal in the sense that it classifies almost all three-band systems, which we have exhaustively studied, finding specific classification surfaces, applying for each one.

Generalization of neural network models for complex network dynamics

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph. Data-driven approximations of differential equations present a promising alternative to traditional methods for uncovering a model of dynamical systems, especially in complex systems that lack explicit first principles. A recently employed machine learning tool for studying dynamics is neural networks, which can be used for solution finding or discovery of differential equations. However, deploying deep learning models in unfamiliar settings-such as predicting dynamics in unobserved state space regions or on novel graphs-can lead to spurious results. Focusing on complex systems whose dynamics are described with a system of first-order differential equations coupled through a graph, we study generalization of neural network predictions in settings where statistical properties of test data and training data are different. We find that neural networks can accurately predict dynamics beyond the immediate training setting within the domain of the training data. To identify when a model is unable to generalize to novel settings, we propose a statistical significance test.

Physical-information model of the immune system as a development of P.K. Anokhin’s theory of functional systems

The article deals with the standard immunological model, which is based on the principles of random combination of molecules and cells and their random encounter with their complementary sites, which is accompanied by the formation of reversible complexes and/or a cascade of subsequent reactions. In its purity, such a model gives rise to various kinds of paradoxes that do not correspond to the reality of immune processes. As a rule, the development of immunology is expressed in the construction of more and more detailed links of immunologic events, but the addition of each new event to the chain of links should lead not to acceleration, but to slowing down of the final process within the combinatorial-complementary system. In this connection, the question of a new possible model of the immune system is raised, which is based on P.K. Anokhin’s theory of functional systems. As its further development the physical-information model (PhIM) of the immune system is proposed, which assumes two plans, informational and physical, of the immune system organization and their coordination on the basis of the ideas of organic potential and processes of conjugation. The information plan is represented as an abstract space of degrees of freedom of the system, analogous to phase space in physics. The current and final state of the system can be represented as points of the state space, the activity of the system with the transition from the current to the final state, as a trajectory in this space. The acceptor of the action result in the theory of functional systems of P.K. Anokhin is connected in this case with the image of the final state as the result of the system action. The construction of the trajectory of the system’s activity can be represented as the direction of reduction of the organic potential of the system, by analogy with that in the case of physical systems and their physical potentials. The organic potential reaches a minimum in the final state and expresses the need of the biosystem as a result of action.

Interpreting the biological effects of protons as a function of physical quantity: linear energy transfer or microdosimetric lineal energy spectrum?

The choice of appropriate physical quantities to characterize the biological effects of ionizing radiation has evolved over time coupled with advances in scientific understanding. The basic hypothesis in radiation dosimetry is that the energy deposited by ionizing radiation initiates all the consequences of exposure in a biological sample (e.g., DNA damage, reproductive cell death). Physical quantities defined to characterize energy deposition have included dose, a measure of the mean energy imparted per unit mass of the target, and linear energy transfer (LET), a measure of the mean energy deposition per unit distance that charged particles traverse in a medium. The primary advantage of using the “dose and LET” physical system is its relative simplicity, especially for presenting and recording results. Inclusion of additional information such as the energy spectrum of charged particles renders this approach adequate to describe the biological effects of large dose levels from homogeneous sources. The primary disadvantage of this system is that it does not provide a unique description of the stochastic nature of radiation interactions. We and others have used dose-averaged LET (LETd) as a correlative physical quantity to the relative biological effectiveness (RBE) of proton beams. This approach is based on established experimental findings that proton RBE increases with LETd. However, this approach might not be applicable to intensity-modulated proton therapy or other applications in which the proton energy spectrum is highly heterogeneous. In the current study, we irradiated cancer cells with scanning proton beams with identical LETd (3.4 keV/µm) but arising from two different proton energy/LET spectra (a narrow spectrum in group 1 and a widespread heterogeneous spectrum in group 2). Clonogenic survival after irradiation revealed significant differences in RBE at any cell surviving fraction: e.g., at a surviving fraction of 0.1, the RBE was 0.97 ± 0.03 in group 1 and 1.16 ± 0.04 in group 2 (p≤0.01), validating our hypothesis that LETd alone may not adequately indicate proton RBE. Further analysis showed that microdosimetric spectrum (the probability density function of the stochastic physical quantity lineal energy y) was helpful for interpreting observed differences in biological effects. However, more accurate use of microdosimetric spectrum to quantify RBE requires a cell line–specific mechanistic model.

Normal Approximation of Random Gaussian Neural Networks

In this paper, we provide explicit upper bounds on some distances between the (law of the) output of a random Gaussian neural network and (the law of) a random Gaussian vector. Our main results concern deep random Gaussian neural networks with a rather general activation function. The upper bounds show how the widths of the layers, the activation function, and other architecture parameters affect the Gaussian approximation of the output. Our techniques, relying on Stein’s method and integration by parts formulas for the Gaussian law, yield estimates on distances that are indeed integral probability metrics and include the convex distance. This latter metric is defined by testing against indicator functions of measurable convex sets and so allows for accurate estimates of the probability that the output is localized in some region of the space, which is an aspect of a significant interest both from a practitioner’s and a theorist’s perspective. We illustrated our results by some numerical examples. Funding: This research was supported by the European Union’s Horizon 2020 research project WARIFA under grant agreement no. 101017385, by the PRIN project 2022 “Variational Analysis of Complex Systems in Materials Science, Physics and Biology” (CUP B53D23009290006), and by the INdAM project “Modelli ed Algoritmi per dati ad elevata dimensionalità” (CUP E53C23001670001).