[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82096-en":3,"doc-seo-82096-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},82096,1374391975076,"Riley","https://ap-avatar.wpscdn.com/avatar/14000253ca4ec9f6853?x-image-process=image/resize,m_fixed,w_180,h_180&k=1783305029341752051",8,"Research & Report","Learning Enabled Parameter Synthesis for Nonlinear Systems from Signal Temporal Logic","Signal Temporal Logic (STL) enables interpretable objectives and constraints for optimal control and learning, particularly when no target time-series data exists. This work proposes learning parameters for nonlinear continuous-time systems with uncertain initial conditions such that they robustly satisfy STL specifications. A gradient-based optimization scheme is combined with set-based reachability verification to efficiently search high-dimensional parameter spaces while providing provable satisfaction guarantees. Experiments on three systems show scalability up to 18 parameter dimensions.","Learning-enabled Parameter Synthesis for Nonlinear Systems  \nfrom Signal Temporal Logic  \nAlex Beaudin 1 ,∗ , Hanna Krasowski 1 ,∗ , Eric Palanques-Tost2 , Calin Belta3 , and Murat Arcak1  \narXiv :2607 .08899v1 [ ee ss . SY] 9 Jul 2026  \nAbstract—Signal Temporal Logic (STL) is increasingly used to describe interpretable objectives and constraints for optimal control and learning methods, especially when no target time series data is available. In this work, we propose to synthesize parameters for nonlinear systems that robustly satisfy continuous-time STL specifications for uncertain initial conditions. To this end, we use gradient-based optimization along with set-based reachability verification to efficiently learn in high-dimensional parameter spaces while providing provable satisfaction guarantees for the optimized parameters. We demonstrate the effectiveness and scalability of our method on three systems with up to 18 parameter dimensions.  \nI. INTRODUCTION  \nTemporal logic is a widespread family of unambiguous and interpretable formal languages. Traditionally, it has been employed in verification with an emphasis on discrete space and time systems. Signal Temporal Logic (STL) [1], [2] describes continuous time and space requirements (specifications) . Beyond verification, STL has been used for controller synthesis [3], [4], monitoring [5], [6], reinforcement learning [7], [8], and parameter synthesis [9], [10] .  \nIn this paper, we present an approach that combines a learning-based algorithm for parameter synthesis from STL with model-based verification (see Fig. 1) . This approach obtains continuous-time satisfaction guarantees for general nonlinear systems with bounded initial conditions by splitting the synthesis into a learning step and a verification step. The learning-based algorithm leverages residual neural ordinary differential equations (NODEs) [11], counter examples, and STL-informed parameter initialization to mitigate the challenges of learning with STL-based loss functions. We show that our approach scales to high state and parameter dimensions on a variety of nonlinear dynamical models. Our main contributions are:  \n• we propose a scalable algorithm to identify parameters of continuous-time nonlinear systems from STL specifications,  \n• we extend the algorithm with a posteriori verification, yielding the same satisfaction assurance as symbolic synthesis methods, and  \n• we demonstrate the proposed algorithm with varying specification complexity and parameter dimensionality.  \n*Equal contribution  \n1 University of California, Berkeley {alex beaudin, krasowski, [arcak](arcak}@berkeley.edu)[}](arcak}@berkeley.edu)[@berkeley.edu](arcak}@berkeley.edu)  \n2 Boston University [ericpt@bu.edu](ericpt@bu.edu)  \n3 University of Maryland, College Park [cbelta@umd.edu](cbelta@umd.edu)  \nThis work was funded in part by the Air Force Office of Scientific Research grant FA5590-23-1-0529 . Alex Beaudin is partially supported by a Fonds de Recherche du Qubec Doctoral Scholarship.  \nII. RELATED WORK  \nParameter synthesis. There are two dominant threads for parameter synthesis from STL specifications: symbolic methods and simulation-based methods. Symbolic methods rely on analytical representations of system dynamics to derive parameter sets with formal satisfaction guarantees. For instance, [12], [13] proposes a recursive set propagation and Bernstein polynomial relaxations to compute parameter regions that provably satisfy the specification. Related approaches exploit domain-specific structures to enable computationally tractable synthesis [14],[15] . While these methods provide strong guarantees, they make strong assumptionson the system dynamics, and the set propagation technique scales poorly with the number of parameters.  \nSimulation-based methods empirically verify satisfaction by evaluating the specification on a finite set of trajectories. Rather than guaranteeing satisfaction, they optimize parameters to satisfy the","cbCaifysaJ3f2Z19","https://ap.wps.com/l/cbCaifysaJ3f2Z19","pdf",1426101,1,6,"English","en",105,"# I. Introduction\n# II. Related Work\n# III. 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problem does the paper address in signal temporal logic?","Question",{"text":74,"@type":75},"The paper addresses how to synthesize parameters for nonlinear continuous-time systems so they robustly satisfy STL specifications when initial conditions are uncertain and no target time-series data is available.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does the proposed method provide satisfaction guarantees?",{"text":79,"@type":75},"It combines gradient-based optimization for learning parameters with set-based reachability verification, using provable guarantees for the optimized parameters rather than relying solely on sampled simulations.",{"name":81,"@type":72,"acceptedAnswer":82},"What scalability results are reported?",{"text":83,"@type":75},"The method is demonstrated on three nonlinear systems with up to 18 parameter dimensions, showing effective learning and tractable verification as specification complexity and dimensionality 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