{"title":"MEP-Net: Generating solutions to scientific problems with limited knowledge by maximum entropy principle.","authors":"Wuyue Yang, Liangrong Peng, Guojie Li, Liu Hong","doi":"10.1063/5.0261211","DOIUrl":"https://doi.org/10.1063/5.0261211","url":null,"abstract":"<p><p>Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions from data. This paper proposes a novel neural network architecture, the MEP-Net, which combines the MEP with neural networks to generate probability distributions from moment constraints. We also provide a comprehensive overview of the fundamentals of the maximum entropy principle, its mathematical formulations, and a rigorous justification for its applicability for non-equilibrium systems based on the large deviations principle. Through fruitful numerical experiments, we demonstrate that the MEP-Net can be particularly useful in modeling the evolution of probability distributions in biochemical reaction networks and in generating complex distributions from data.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145130102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Gerard McCaul, Juan Sebastian Totero Gongora, Wendy Otieno, Sergey Savel'ev, Alexandre Zagoskin, Alexander G Balanov
{"title":"Minimal quantum reservoirs with Hamiltonian encoding.","authors":"Gerard McCaul, Juan Sebastian Totero Gongora, Wendy Otieno, Sergey Savel'ev, Alexandre Zagoskin, Alexander G Balanov","doi":"10.1063/5.0282921","DOIUrl":"https://doi.org/10.1063/5.0282921","url":null,"abstract":"<p><p>We investigate a minimal architecture for quantum reservoir computing based on Hamiltonian encoding, in which input data are injected via modulation of system parameters rather than state preparation. This approach circumvents many of the experimental overheads typically associated with quantum machine learning, enabling computation without feedback, memory, or state tomography. We demonstrate that such a minimal quantum reservoir, despite lacking intrinsic memory, can perform nonlinear regression and prediction tasks when augmented with post-processing delay embeddings. Our results provide a conceptually and practically streamlined framework for quantum information processing, offering a clear baseline for future implementations on near-term quantum hardware.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145063637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamics-informed reservoir computing with visibility graphs.","authors":"Charlotte Geier, Rasha Shanaz, Merten Stender","doi":"10.1063/5.0293030","DOIUrl":"https://doi.org/10.1063/5.0293030","url":null,"abstract":"<p><p>Accurate prediction of complex and nonlinear time series remains a challenging problem across engineering and scientific disciplines. Reservoir computing (RC) offers a computationally efficient alternative to traditional deep learning by training only the readout layer while employing a randomly structured and fixed reservoir network. Despite its advantages, the largely random reservoir graph architecture often results in suboptimal and oversized networks with poorly understood dynamics. Addressing this issue, we propose a novel Dynamics-Informed Reservoir Computing (DyRC) framework that systematically infers the reservoir network structure directly from the input training sequence. This work proposes to employ the visibility graph (VG) technique, which converts time series data into networks by representing measurement points as nodes linked by mutual visibility. The reservoir network is constructed by directly adopting the VG network from a training data sequence, leveraging the parameter-free visibility graph approach to avoid expensive hyperparameter tuning. This process results in a reservoir that is directly informed by the specific dynamics of the prediction task under study. We assess the DyRC-VG method through prediction tasks involving the canonical nonlinear Duffing oscillator, evaluating prediction accuracy and consistency. Compared to an Erdős-Rényi (ER) graph of the same size, spectral radius, and fixed density, we observe higher prediction quality and more consistent performance over repeated implementations in the DyRC-VG. An ER graph with density matched to the DyRC-VG can in some conditions outperform both approaches.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145079614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ying Xie, Xuening Li, Xueqin Wang, Zhiqiu Ye, Lijian Yang, Ya Jia
{"title":"Energy-induced chimera-like states in bilayer memristive FitzHugh-Nagumo neural networks.","authors":"Ying Xie, Xuening Li, Xueqin Wang, Zhiqiu Ye, Lijian Yang, Ya Jia","doi":"10.1063/5.0285156","DOIUrl":"https://doi.org/10.1063/5.0285156","url":null,"abstract":"<p><p>Despite extensive efforts to analyze synchronization and chimera states, it is limited to understand their emergence from an energy-based perspective in multilayer network synchronization. In this study, the bilayer FitzHugh-Nagumo neural network is constructed and the heterogeneity is realized by distinct dynamics of periodic and chaotic firing patterns. By analyzing the energy patterns of neurons, it is discovered that the intralayer synchronization is independent of the interlayer coupling in networks. Under specific conditions of intralayer coupling strength and nearest-neighbor connectivity, periodic neurons with a small energy difference give rise to chimera-like states. Meanwhile, chaotic neurons with a large energy difference induce a traveling phase-wave pattern. Furthermore, nonlocal coupling with proper synaptic strength leads to the emergence of a strong chimera-like state, which maintains energy between the energies of synchronized and desynchronized cases. The results uncover an energy-driven mechanism underlying the emergence of complex collective behaviors in multilayer neuronal systems, and it offers potential guidance for designing energy-efficient neuromorphic circuits.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145085282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantization induced memory-nonlinearity transfer: Implications of analog-to-digital conversion in reservoir computing.","authors":"Max Austin, Kohei Nakajima","doi":"10.1063/5.0273403","DOIUrl":"10.1063/5.0273403","url":null,"abstract":"<p><p>The output-side behaviors of typical digital computing systems, such as simulated neural networks, are generally unaffected by the act of observation; however, this is not the case for the burgeoning field of physical reservoir computers (PRCs). Observer dynamics can limit or modify the natural state information of a PRC in many ways, and among the most common is the conversion from analog to digital data needed for calculations. Here, to aid in the development of novel PRCs, we investigate the effects of bounded, quantized observations on systems' natural computational abilities. By utilizing a classical reservoir computing (RC) (an echo-state network) and some PRCs (a pneumatic artificial muscle and a soft tentacle), we show that observed state quantization effectively converts a system's natural memory into higher-order, nonlinear dynamics. Furthermore, this same effect can assist in reducing detectable system errors in the presence of noise. We demonstrate how these effects, imposed only through output-end observations, can improve timer task robustness, target different computational task types, and even encode the chaotic dynamics of a Lorenz attractor in a simple linear RC in a closed loop.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144999707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dissipative solitons onset through modulational instability of the cubic complex Ginzburg-Landau equation with nonlinear gradients.","authors":"M I Carvalho, M Facão, Orazio Descalzi","doi":"10.1063/5.0278588","DOIUrl":"https://doi.org/10.1063/5.0278588","url":null,"abstract":"<p><p>Modulation instability (MI) of the continuous wave (cw) has been associated with the onset of stable solitons in conservative and dissipative systems. The cubic complex Ginzburg-Landau equation (CGLE) is a prototype of a damped, driven, nonlinear, and dispersive system. The inclusion of nonlinear gradients is essential to stabilize pulses whether stationary or oscillatory. The soliton solutions of this model have been reasonably studied; however, its cw solution characteristics and stability have not been reported yet. Here, we obtain the cw solutions of the cubic CGLE with nonlinear gradient terms and study its short- and long-term evolution under the effect of small perturbations. We have found that, for each admissible amplitude, there are two branches of cw solutions, and all of them are unstable. Then, through direct integration of the evolution equation, we study the evolution of those cw solutions, observing the emergence of plain and oscillatory solitons. Depending on whether the cw and/or its perturbation are sinusoidal, we can obtain a train of a finite number of pulses or bound states.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144999716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Minimal deterministic echo state networks outperform random reservoirs in learning chaotic dynamics.","authors":"F Martinuzzi","doi":"10.1063/5.0288751","DOIUrl":"https://doi.org/10.1063/5.0288751","url":null,"abstract":"<p><p>Machine learning (ML) is widely used to model chaotic systems. Among ML approaches, echo state networks (ESNs) have received considerable attention due to their simple construction and fast training. However, ESN performance is highly sensitive to hyperparameter choices and to its random initialization. In this work, we demonstrate that ESNs constructed using simple rules and deterministic topologies [minimal complexity ESNs (MESNs)] outperform standard ESNs in the task of chaotic attractor reconstruction. We use a dataset of more than 90 chaotic systems to benchmark 10 different minimal deterministic reservoir initializations. We find that MESNs obtain up to a 41% reduction in error compared to standard ESNs. Furthermore, we show that the MESNs are more robust, exhibiting less inter-run variation, and have the ability to reuse hyperparameters across different systems. Our results illustrate how structured simplicity in ESN design can outperform stochastic complexity in learning chaotic dynamics.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144999740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Adaptive control of dynamical systems using reservoir computing.","authors":"Swarnendu Mandal, Swati Chauhan, Umesh Kumar Verma, Manish Dev Shrimali, Kazuyuki Aihara","doi":"10.1063/5.0291585","DOIUrl":"https://doi.org/10.1063/5.0291585","url":null,"abstract":"<p><p>We demonstrate a data-driven technique for adaptive control of dynamical systems that exploits the reservoir computing method. We show that a reservoir computer can be trained to predict a system parameter from the time series. Subsequently, a control signal based on the predicted parameter can be used as a feedback to the dynamical system to lead it to a target state. Our results show that the dynamical system can be controlled throughout a wide range of attractor types. One set of training data consisting of only a few time series corresponding to the known parameter values enables our scheme to control a dynamical system to an arbitrary target attractor starting from any other initial attractor. In addition to numerical results, we implement our scheme in real-world systems, such as a Rössler system, realized in an electronic circuit to demonstrate the effectiveness of our approach.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144991628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Christophe Letellier, Ludovico Minati, Jean-Pierre Barbot, Irene Sendiña-Nadal, I Leyva
{"title":"Flatness-based control for generalized synchronization of chaotic systems with large dissipation and dimension mismatch.","authors":"Christophe Letellier, Ludovico Minati, Jean-Pierre Barbot, Irene Sendiña-Nadal, I Leyva","doi":"10.1063/5.0276030","DOIUrl":"https://doi.org/10.1063/5.0276030","url":null,"abstract":"<p><p>A flat control law is based on the structural analysis of a controlled system, allowing optimal placement of sensors and actuators. Once designed, any desired dynamics can be imposed onto the system. When the target dynamics comes from a system structurally different from the controlled one, generalized synchronization can be achieved, provided the control gain is sufficiently large. As the gain increases, various relationships emerge between the drive and response systems, depending on differences in their dimensions and dissipation rates. The principal contribution of this work lies in the exploration of drive-response system pairs with varying dimensions (ranging from 2 to 4) and dissipation levels, including combinations of dissipative and conservative systems. We identify several types of generalized synchronization, using a classification based on the thickness of the resulting Lissajous curves and the lack of conjugacy between the first-return maps of the drive and response systems.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145013967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Controlling complex rhythms: A hierarchical approach to limit cycle switching.","authors":"Suvam Pal, Dibakar Ghosh, Sandip Saha","doi":"10.1063/5.0296708","DOIUrl":"https://doi.org/10.1063/5.0296708","url":null,"abstract":"<p><p>Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering oscillations. The presence of multiple concentric limit cycles reflects distinct behavioral symmetries within a system. In this work, we investigate the hierarchical dynamical transitions from one limit cycle to another, driven by oscillatory excitation while preserving other system properties. We demonstrate that controlling multirhythmicity through hierarchical, stepwise periodic modulation enables reliable switching between rhythmic states. This hierarchical control framework is crucial for applications in neuro-engineering and synthetic biology, where precise, robust modulation of complex rhythmic behaviors enhances system functionality and adaptability.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 9","pages":""},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145032860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}