Pub Date : 2025-11-17DOI: 10.1038/s43588-025-00901-x
Fiona R. Kolbinger, Jakob Nikolas Kather
Technical metrics used to evaluate medical artificial intelligence tools often fail to predict their clinical impact. We characterize this discordance and propose a framework of study designs to guide the translational process for clinical artificial intelligence tools, acknowledging their diversity and specific validation requirements.
{"title":"Adaptive validation strategies for real-world clinical artificial intelligence","authors":"Fiona R. Kolbinger, Jakob Nikolas Kather","doi":"10.1038/s43588-025-00901-x","DOIUrl":"10.1038/s43588-025-00901-x","url":null,"abstract":"Technical metrics used to evaluate medical artificial intelligence tools often fail to predict their clinical impact. We characterize this discordance and propose a framework of study designs to guide the translational process for clinical artificial intelligence tools, acknowledging their diversity and specific validation requirements.","PeriodicalId":74246,"journal":{"name":"Nature computational science","volume":"5 11","pages":"980-986"},"PeriodicalIF":18.3,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145544296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-14DOI: 10.1038/s43588-025-00898-3
Yi-Xin Sha, Ming-Yao Xia, Ling Lu, Yi Yang
Topological photonics and acoustics have attracted wide research interest for their ability to manipulate light and sound at surfaces. The supercell technique is the conventional standard approach used to calculate these boundary effects, but, as the supercell grows in size, this method requires increasingly large computational resources. Additionally, it falls short in differentiating the surface states at opposite boundaries and, due to finite-size effects, from bulk states. Here, to overcome these limitations, we provide two complementary efficient methods for obtaining the ideal topological surface states of semi-infinite systems of diverse surface configurations. The first is the cyclic reduction method, which is based on iteratively inverting the Hamiltonian for a single unit cell, and the other is the transfer matrix method, which relies on eigenanalysis of a transfer matrix for a pair of unit cells. Numerical benchmarks, including gyromagnetic photonic crystals, valley photonic crystals, spin-Hall acoustic crystals and quadrupole photonic crystals, jointly show that both methods can effectively sort out the boundary modes via the surface density of states, at reduced computational cost and increased speed. Our computational schemes enable direct comparisons with near-field scanning measurements, thereby expediting the exploration of topological artificial materials and the design of topological devices. This study reports two efficient methods—cyclic reduction and transfer matrix—to compute topological surface states in photonic and acoustic systems, cutting memory and time use by up to 100-fold and enabling the faster design of advanced topological devices.
{"title":"Efficient algorithms for the surface density of states in topological photonic and acoustic systems","authors":"Yi-Xin Sha, Ming-Yao Xia, Ling Lu, Yi Yang","doi":"10.1038/s43588-025-00898-3","DOIUrl":"10.1038/s43588-025-00898-3","url":null,"abstract":"Topological photonics and acoustics have attracted wide research interest for their ability to manipulate light and sound at surfaces. The supercell technique is the conventional standard approach used to calculate these boundary effects, but, as the supercell grows in size, this method requires increasingly large computational resources. Additionally, it falls short in differentiating the surface states at opposite boundaries and, due to finite-size effects, from bulk states. Here, to overcome these limitations, we provide two complementary efficient methods for obtaining the ideal topological surface states of semi-infinite systems of diverse surface configurations. The first is the cyclic reduction method, which is based on iteratively inverting the Hamiltonian for a single unit cell, and the other is the transfer matrix method, which relies on eigenanalysis of a transfer matrix for a pair of unit cells. Numerical benchmarks, including gyromagnetic photonic crystals, valley photonic crystals, spin-Hall acoustic crystals and quadrupole photonic crystals, jointly show that both methods can effectively sort out the boundary modes via the surface density of states, at reduced computational cost and increased speed. Our computational schemes enable direct comparisons with near-field scanning measurements, thereby expediting the exploration of topological artificial materials and the design of topological devices. This study reports two efficient methods—cyclic reduction and transfer matrix—to compute topological surface states in photonic and acoustic systems, cutting memory and time use by up to 100-fold and enabling the faster design of advanced topological devices.","PeriodicalId":74246,"journal":{"name":"Nature computational science","volume":"5 12","pages":"1192-1201"},"PeriodicalIF":18.3,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145524776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In recent years, artificial intelligence has advanced the design–make–test–analyze cycle, transforming molecular discovery. Despite these advances, the compartmentalized approach to computer-aided molecular design and synthesis remains a critical bottleneck, limiting further optimization of the design–make–test–analyze cycle. Here, to this end, we introduce SynGFN, which models molecular design as a cascade of simulated chemical reactions, enabling the assembly of molecules from synthesizable building blocks. SynGFN features two key ingredients: (1) a hierarchically pretrained policy network that accelerates learning across diverse distributions of desirable molecules in chemical spaces, and (2) a multifidelity acquisition framework to alleviate the cost of reward evaluations. These technical developments collectively endow SynGFN with the capability to explore a chemical space up to an order of magnitude larger (measured in terms of #Circles) than that of other synthesis-aware generative models, while identifying the most diverse, synthesizable and high-performance molecules. We demonstrate SynGFN’s potential impacts by designing inhibitors for GluN1/GluN3A, a therapeutic target for neuropsychiatric disorders. A persistent gap from theoretical molecules to experimentally viable compounds has hindered the practical adoption of generative algorithms. This study proposes SynGFN as a bridge linking molecular design and synthesis, accelerating exploration and producing diverse, synthesizable, high-performance molecules.
{"title":"SynGFN: learning across chemical space with generative flow-based molecular discovery","authors":"Yuchen Zhu, Shuwang Li, Jihong Chen, Donghai Zhao, Xiaorui Wang, Yitong Li, Yifei Liu, Yue Kong, Beichen Zhang, Chang Liu, Tingjun Hou, Chang-Yu Hsieh","doi":"10.1038/s43588-025-00902-w","DOIUrl":"10.1038/s43588-025-00902-w","url":null,"abstract":"In recent years, artificial intelligence has advanced the design–make–test–analyze cycle, transforming molecular discovery. Despite these advances, the compartmentalized approach to computer-aided molecular design and synthesis remains a critical bottleneck, limiting further optimization of the design–make–test–analyze cycle. Here, to this end, we introduce SynGFN, which models molecular design as a cascade of simulated chemical reactions, enabling the assembly of molecules from synthesizable building blocks. SynGFN features two key ingredients: (1) a hierarchically pretrained policy network that accelerates learning across diverse distributions of desirable molecules in chemical spaces, and (2) a multifidelity acquisition framework to alleviate the cost of reward evaluations. These technical developments collectively endow SynGFN with the capability to explore a chemical space up to an order of magnitude larger (measured in terms of #Circles) than that of other synthesis-aware generative models, while identifying the most diverse, synthesizable and high-performance molecules. We demonstrate SynGFN’s potential impacts by designing inhibitors for GluN1/GluN3A, a therapeutic target for neuropsychiatric disorders. A persistent gap from theoretical molecules to experimentally viable compounds has hindered the practical adoption of generative algorithms. This study proposes SynGFN as a bridge linking molecular design and synthesis, accelerating exploration and producing diverse, synthesizable, high-performance molecules.","PeriodicalId":74246,"journal":{"name":"Nature computational science","volume":"6 1","pages":"29-38"},"PeriodicalIF":18.3,"publicationDate":"2025-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145514834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-12DOI: 10.1038/s43588-025-00905-7
Samuel A. Nastase
A systematic comparison of large language models suggests that larger models align better with both human behavior and brain activity during natural reading. Instruction tuning, however, does not yield a similar benefit.
{"title":"Larger language models better align with the reading brain","authors":"Samuel A. Nastase","doi":"10.1038/s43588-025-00905-7","DOIUrl":"10.1038/s43588-025-00905-7","url":null,"abstract":"A systematic comparison of large language models suggests that larger models align better with both human behavior and brain activity during natural reading. Instruction tuning, however, does not yield a similar benefit.","PeriodicalId":74246,"journal":{"name":"Nature computational science","volume":"5 11","pages":"994-995"},"PeriodicalIF":18.3,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145508432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-04DOI: 10.1038/s43588-025-00897-4
Yiqing Zhou, Chao Wan, Yichen Xu, Jin Peng Zhou, Kilian Q. Weinberger, Eun-Ah Kim
As quantum hardware advances toward enabling error-corrected quantum circuits in the near future, the absence of an efficient polynomial-time decoding algorithm for logical circuits presents a critical bottleneck. While quantum memory decoding has been well studied, inevitable correlated errors introduced by transversal entangling logical gates prevent the straightforward generalization of quantum memory decoders. Here we introduce a data-centric, modular decoder framework, the Multi-Core Circuit Decoder (MCCD), which consists of decoder modules corresponding to each logical operation supported by the quantum hardware. The MCCD handles both single-qubit and entangling gates within a unified framework. We train MCCD using mirror-symmetric random Clifford circuits, demonstrating its ability to effectively learn correlated decoding patterns. Through extensive testing on circuits substantially deeper than those used in training, we show that MCCD maintains high logical accuracy while exhibiting competitive polynomial decoding time across increasing circuit depths and code distances. When compared with conventional decoders such as minimum weight perfect matching (MWPM), most likely error (MLE) and belief propagation with ordered statistics post-processing (BP-OSD), MCCD achieves competitive accuracy with substantially better time efficiency, particularly for circuits with entangling gates. Our approach provides a noise-model-agnostic solution to the decoding challenge in deep logical quantum circuits. This study reports a machine learning decoder that efficiently corrects errors in quantum logical circuits with entangling gates. The Multi-Core Circuit Decoder achieves competitive accuracy while running much faster than conventional methods.
随着量子硬件在不久的将来向纠错量子电路的方向发展，缺乏有效的逻辑电路多项式时间解码算法是一个关键的瓶颈。虽然量子记忆译码已经得到了很好的研究，但横向纠缠逻辑门引入的不可避免的相关误差阻碍了量子记忆译码器的直接推广。在这里，我们介绍了一个以数据为中心的模块化解码器框架，即多核电路解码器（MCCD），它由与量子硬件支持的每个逻辑运算相对应的解码器模块组成。MCCD在一个统一的框架内处理单量子位和纠缠门。我们使用镜像对称随机Clifford电路训练MCCD，证明了其有效学习相关解码模式的能力。通过在比训练中使用的电路更深的电路上进行广泛的测试，我们表明MCCD在保持高逻辑准确性的同时，在增加电路深度和代码距离时表现出具有竞争力的多项式解码时间。与传统的解码器(如最小权重完美匹配（MWPM），最可能误差（MLE）和有序统计后处理（BP-OSD）的信念传播（belief propagation with ordered statistics postprocessing, BP-OSD）相比，MCCD实现了具有竞争力的精度和更好的时间效率，特别是对于有纠缠门的电路。我们的方法为深度逻辑量子电路中的解码挑战提供了一种与噪声模型无关的解决方案。
{"title":"Learning to decode logical circuits","authors":"Yiqing Zhou, Chao Wan, Yichen Xu, Jin Peng Zhou, Kilian Q. Weinberger, Eun-Ah Kim","doi":"10.1038/s43588-025-00897-4","DOIUrl":"10.1038/s43588-025-00897-4","url":null,"abstract":"As quantum hardware advances toward enabling error-corrected quantum circuits in the near future, the absence of an efficient polynomial-time decoding algorithm for logical circuits presents a critical bottleneck. While quantum memory decoding has been well studied, inevitable correlated errors introduced by transversal entangling logical gates prevent the straightforward generalization of quantum memory decoders. Here we introduce a data-centric, modular decoder framework, the Multi-Core Circuit Decoder (MCCD), which consists of decoder modules corresponding to each logical operation supported by the quantum hardware. The MCCD handles both single-qubit and entangling gates within a unified framework. We train MCCD using mirror-symmetric random Clifford circuits, demonstrating its ability to effectively learn correlated decoding patterns. Through extensive testing on circuits substantially deeper than those used in training, we show that MCCD maintains high logical accuracy while exhibiting competitive polynomial decoding time across increasing circuit depths and code distances. When compared with conventional decoders such as minimum weight perfect matching (MWPM), most likely error (MLE) and belief propagation with ordered statistics post-processing (BP-OSD), MCCD achieves competitive accuracy with substantially better time efficiency, particularly for circuits with entangling gates. Our approach provides a noise-model-agnostic solution to the decoding challenge in deep logical quantum circuits. This study reports a machine learning decoder that efficiently corrects errors in quantum logical circuits with entangling gates. The Multi-Core Circuit Decoder achieves competitive accuracy while running much faster than conventional methods.","PeriodicalId":74246,"journal":{"name":"Nature computational science","volume":"5 12","pages":"1158-1167"},"PeriodicalIF":18.3,"publicationDate":"2025-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.comhttps://www.nature.com/articles/s43588-025-00897-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145446737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-31DOI: 10.1038/s43588-025-00899-2
Alexandre Mojon, Robert Mahari, Sandro Claudio Lera
Selecting capable counsel can shape the outcome of litigation, yet evaluating law firm performance remains challenging. Widely used rankings prioritize prestige, size and revenue over empirical litigation outcomes, offering little practical guidance. Here, to address this gap, we build on the Bradley–Terry model and introduce a new ranking framework that treats each lawsuit as a competitive game between plaintiff and defendant law firms. Leveraging a newly constructed dataset of 60,540 US civil lawsuits involving 54,541 law firms, our findings show that existing reputation-based rankings correlate poorly with actual litigation success, while our outcome-based ranking substantially improves predictive accuracy. These findings establish a foundation for more transparent, data-driven assessments of legal performance. This study introduces a data-driven method for ranking law firms based on litigation outcomes, revealing that traditional reputation-based rankings do not reflect legal performance accurately.
{"title":"Data-driven law firm rankings to reduce information asymmetry in legal disputes","authors":"Alexandre Mojon, Robert Mahari, Sandro Claudio Lera","doi":"10.1038/s43588-025-00899-2","DOIUrl":"10.1038/s43588-025-00899-2","url":null,"abstract":"Selecting capable counsel can shape the outcome of litigation, yet evaluating law firm performance remains challenging. Widely used rankings prioritize prestige, size and revenue over empirical litigation outcomes, offering little practical guidance. Here, to address this gap, we build on the Bradley–Terry model and introduce a new ranking framework that treats each lawsuit as a competitive game between plaintiff and defendant law firms. Leveraging a newly constructed dataset of 60,540 US civil lawsuits involving 54,541 law firms, our findings show that existing reputation-based rankings correlate poorly with actual litigation success, while our outcome-based ranking substantially improves predictive accuracy. These findings establish a foundation for more transparent, data-driven assessments of legal performance. This study introduces a data-driven method for ranking law firms based on litigation outcomes, revealing that traditional reputation-based rankings do not reflect legal performance accurately.","PeriodicalId":74246,"journal":{"name":"Nature computational science","volume":"5 11","pages":"1010-1016"},"PeriodicalIF":18.3,"publicationDate":"2025-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.comhttps://www.nature.com/articles/s43588-025-00899-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145423744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-31DOI: 10.1038/s43588-025-00827-4
Aurelia Tamò-Larrieux, Clement Guitton, Simon Mayer
A recent study highlights how data changes not only how we can assess the performance of legal firms in the US, but more broadly how computational science is expanding beyond its traditional scope and into the legal field.
{"title":"A computational science perspective on the legal system","authors":"Aurelia Tamò-Larrieux, Clement Guitton, Simon Mayer","doi":"10.1038/s43588-025-00827-4","DOIUrl":"10.1038/s43588-025-00827-4","url":null,"abstract":"A recent study highlights how data changes not only how we can assess the performance of legal firms in the US, but more broadly how computational science is expanding beyond its traditional scope and into the legal field.","PeriodicalId":74246,"journal":{"name":"Nature computational science","volume":"5 11","pages":"990-991"},"PeriodicalIF":18.3,"publicationDate":"2025-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145423722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Advancements in spatial omics permit spatially resolved measurements across several biological modalities. The high cost of acquiring co-profiled multimodal data limits the analysis. This underscores the necessity for computational methods to integrate unpaired spatial multi-omics data and perform cross-modal predictions on single-modality data. The integration of spatial omics is challenging due to typically low signal-to-noise ratios. Here we introduce SWITCH (Spatially Weighted Multi-omics Integration and Cross-modal Translation with Cycle-mapping Harmonization), a deep generative model for spatial multi-omics integration. SWITCH presents a cycle-mapping mechanism that produces dependable cross-modal translations without requiring additional paired data. These cross-modal translations function as pseudo-pairs to provide supplementary signals. Systematic evaluations demonstrate that SWITCH outperforms existing methods in terms of integration accuracy and achieves more precise spatial domain delineation, resolving brain cortical structures at higher resolution. The reliability of cross-modal translations was validated, facilitating various downstream analyses such as differential analysis, trajectory inference and gene regulatory network inference. In this study the authors present SWITCH, a deep learning model that integrates unpaired spatial multi-omics data and enables unsupervised cross-modal prediction, aiding spatial domain identification and downstream biological analysis.
空间组学的进步允许跨几种生物模式进行空间分辨测量。获取共剖面多模态数据的高成本限制了分析。这强调了计算方法整合非配对空间多组学数据和对单模态数据进行跨模态预测的必要性。由于典型的低信噪比，空间组学的集成具有挑战性。本文介绍了空间多组学集成的深度生成模型SWITCH （spatial Weighted Multi-omics Integration and Cross-modal Translation with cycle mapping Harmonization）。SWITCH提供了一种循环映射机制，可以产生可靠的跨模态翻译，而不需要额外的成对数据。这些跨模态翻译作为伪对来提供补充信号。系统评估表明，SWITCH在整合精度方面优于现有方法，可以实现更精确的空间域描绘，以更高的分辨率解析大脑皮层结构。验证了跨模态翻译的可靠性，为差分分析、轨迹推断和基因调控网络推断等下游分析提供了便利。
{"title":"Integrative deep learning of spatial multi-omics with SWITCH","authors":"Zhongzhan Li, Sanqing Qu, Haixin Liang, Ruohui Tang, Xudong Zhang, Fan Lu, Jiani Yang, Ziling Gan, Shaorong Gao, Yanping Zhang, Guang Chen","doi":"10.1038/s43588-025-00891-w","DOIUrl":"10.1038/s43588-025-00891-w","url":null,"abstract":"Advancements in spatial omics permit spatially resolved measurements across several biological modalities. The high cost of acquiring co-profiled multimodal data limits the analysis. This underscores the necessity for computational methods to integrate unpaired spatial multi-omics data and perform cross-modal predictions on single-modality data. The integration of spatial omics is challenging due to typically low signal-to-noise ratios. Here we introduce SWITCH (Spatially Weighted Multi-omics Integration and Cross-modal Translation with Cycle-mapping Harmonization), a deep generative model for spatial multi-omics integration. SWITCH presents a cycle-mapping mechanism that produces dependable cross-modal translations without requiring additional paired data. These cross-modal translations function as pseudo-pairs to provide supplementary signals. Systematic evaluations demonstrate that SWITCH outperforms existing methods in terms of integration accuracy and achieves more precise spatial domain delineation, resolving brain cortical structures at higher resolution. The reliability of cross-modal translations was validated, facilitating various downstream analyses such as differential analysis, trajectory inference and gene regulatory network inference. In this study the authors present SWITCH, a deep learning model that integrates unpaired spatial multi-omics data and enables unsupervised cross-modal prediction, aiding spatial domain identification and downstream biological analysis.","PeriodicalId":74246,"journal":{"name":"Nature computational science","volume":"5 11","pages":"1051-1063"},"PeriodicalIF":18.3,"publicationDate":"2025-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145402993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-24DOI: 10.1038/s43588-025-00873-y
Ayse Kotil, Elijah Pelofske, Stephanie Riedmüller, Daniel J. Egger, Stephan Eidenbenz, Thorsten Koch, Stefan Woerner
The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, that is, the set of all Pareto-optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. Here we use a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum-cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with matrix product state numerical simulation, and show its potential to outperform classical approaches. This study explores the use of quantum computing to address multi-objective optimization challenges. By using a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of multi-objective weighted max-cut problems, the authors demonstrate promising results—both in simulation and on IBM Quantum hardware—surpassing classical approaches.
{"title":"Quantum approximate multi-objective optimization","authors":"Ayse Kotil, Elijah Pelofske, Stephanie Riedmüller, Daniel J. Egger, Stephan Eidenbenz, Thorsten Koch, Stefan Woerner","doi":"10.1038/s43588-025-00873-y","DOIUrl":"10.1038/s43588-025-00873-y","url":null,"abstract":"The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, that is, the set of all Pareto-optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. Here we use a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum-cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with matrix product state numerical simulation, and show its potential to outperform classical approaches. This study explores the use of quantum computing to address multi-objective optimization challenges. By using a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of multi-objective weighted max-cut problems, the authors demonstrate promising results—both in simulation and on IBM Quantum hardware—surpassing classical approaches.","PeriodicalId":74246,"journal":{"name":"Nature computational science","volume":"5 12","pages":"1168-1177"},"PeriodicalIF":18.3,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.comhttps://www.nature.com/articles/s43588-025-00873-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145369252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-23DOI: 10.1038/s43588-025-00893-8
Zihan Yu, Jingtao Ding, Yong Li
Network dynamics are fundamental to analyzing the properties of high-dimensional complex systems and understanding their behavior. Despite the accumulation of observational data across many domains, mathematical models exist in only a few areas with clear underlying principles. Here we show that a neural symbolic regression approach can bridge this gap by automatically deriving formulas from data. Our method reduces searches on high-dimensional networks to equivalent one-dimensional systems and uses pretrained neural networks to guide accurate formula discovery. Applied to ten benchmark systems, it recovers the correct forms and parameters of underlying dynamics. In two empirical natural systems, it corrects existing models of gene regulation and microbial communities, reducing prediction error by 59.98% and 55.94%, respectively. In epidemic transmission across human mobility networks of various scales, it discovers dynamics that exhibit the same power-law distribution of node correlations across scales and reveal country-level differences in intervention effects. These results demonstrate that machine-driven discovery of network dynamics can enhance understandings of complex systems and advance the development of complexity science.
{"title":"Discovering network dynamics with neural symbolic regression.","authors":"Zihan Yu, Jingtao Ding, Yong Li","doi":"10.1038/s43588-025-00893-8","DOIUrl":"10.1038/s43588-025-00893-8","url":null,"abstract":"<p><p>Network dynamics are fundamental to analyzing the properties of high-dimensional complex systems and understanding their behavior. Despite the accumulation of observational data across many domains, mathematical models exist in only a few areas with clear underlying principles. Here we show that a neural symbolic regression approach can bridge this gap by automatically deriving formulas from data. Our method reduces searches on high-dimensional networks to equivalent one-dimensional systems and uses pretrained neural networks to guide accurate formula discovery. Applied to ten benchmark systems, it recovers the correct forms and parameters of underlying dynamics. In two empirical natural systems, it corrects existing models of gene regulation and microbial communities, reducing prediction error by 59.98% and 55.94%, respectively. In epidemic transmission across human mobility networks of various scales, it discovers dynamics that exhibit the same power-law distribution of node correlations across scales and reveal country-level differences in intervention effects. These results demonstrate that machine-driven discovery of network dynamics can enhance understandings of complex systems and advance the development of complexity science.</p>","PeriodicalId":74246,"journal":{"name":"Nature computational science","volume":" ","pages":""},"PeriodicalIF":18.3,"publicationDate":"2025-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145356974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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