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2021 - Universal Differential Equations for Scientific Machine Learning.pdf", "md5": "47392d78bcbba248c54e1db4875e7de6", "mtime": 1745330589349, "tags": [], "relations": {}, "dateAdded": "2025-04-22T14:03:09Z", "dateModified": "2025-04-22T14:03:09Z" } }, { "key": "TXKJJQ3X", "version": 440, "library": { "type": "group", "id": 362459, "name": "DynElasticNet", "links": { "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/362459/items/TXKJJQ3X", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet/items/TXKJJQ3X", "type": "text/html" }, "up": { "href": "https://api.zotero.org/groups/362459/items/NE6A4ZH5", "type": "application/json" } }, "meta": { "createdByUser": { "id": 1366190, "username": "kschischo", "name": "Maik Kschischo", "links": { "alternate": { "href": "https://www.zotero.org/kschischo", "type": "text/html" } } }, "numChildren": 0 }, "data": { "key": "TXKJJQ3X", "version": 440, "parentItem": "NE6A4ZH5", "itemType": "note", "note": "Comment: 5 figures, 2 tables, 11 supplemental figures, 29 pages, 25 supplemental pages", "tags": [], "relations": {}, "dateAdded": "2025-04-22T14:03:07Z", "dateModified": "2025-04-22T14:03:07Z" } }, { "key": "NE6A4ZH5", "version": 440, "library": { "type": "group", "id": 362459, "name": "DynElasticNet", "links": { "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/362459/items/NE6A4ZH5", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet/items/NE6A4ZH5", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1366190, "username": "kschischo", "name": "Maik Kschischo", "links": { "alternate": { "href": "https://www.zotero.org/kschischo", "type": "text/html" } } }, "creatorSummary": "Rackauckas et al.", "parsedDate": "2021-11-02", "numChildren": 3 }, "data": { "key": "NE6A4ZH5", "version": 440, "itemType": "preprint", "title": "Universal Differential Equations for Scientific Machine Learning", "creators": [ { "creatorType": "author", "firstName": "Christopher", "lastName": "Rackauckas" }, { "creatorType": "author", "firstName": "Yingbo", "lastName": "Ma" }, { "creatorType": "author", "firstName": "Julius", "lastName": "Martensen" }, { "creatorType": "author", "firstName": "Collin", "lastName": "Warner" }, { "creatorType": "author", "firstName": "Kirill", "lastName": "Zubov" }, { "creatorType": "author", "firstName": "Rohit", "lastName": "Supekar" }, { "creatorType": "author", "firstName": "Dominic", "lastName": "Skinner" }, { "creatorType": "author", "firstName": "Ali", "lastName": "Ramadhan" }, { "creatorType": "author", "firstName": "Alan", "lastName": "Edelman" } ], "abstractNote": "In the context of science, the well-known adage \"a picture is worth a thousand words\" might well be \"a model is worth a thousand datasets.\" In this manuscript we introduce the SciML software ecosystem as a tool for mixing the information of physical laws and scientific models with data-driven machine learning approaches. We describe a mathematical object, which we denote universal differential equations (UDEs), as the unifying framework connecting the ecosystem. We show how a wide variety of applications, from automatically discovering biological mechanisms to solving high-dimensional Hamilton-Jacobi-Bellman equations, can be phrased and efficiently handled through the UDE formalism and its tooling. We demonstrate the generality of the software tooling to handle stochasticity, delays, and implicit constraints. This funnels the wide variety of SciML applications into a core set of training mechanisms which are highly optimized, stabilized for stiff equations, and compatible with distributed parallelism and GPU accelerators.", "genre": "", "repository": "arXiv", "archiveID": "arXiv:2001.04385", "place": "", "date": "2021-11-02", "series": "", "seriesNumber": "", "DOI": "10.48550/arXiv.2001.04385", "citationKey": "", "url": "http://arxiv.org/abs/2001.04385", "accessDate": "2025-04-22T14:03:07Z", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "", "libraryCatalog": "arXiv.org", "callNumber": "", "rights": "", "extra": "arXiv:2001.04385 [cs]", "tags": [ { "tag": "Computer Science - Machine Learning", "type": 1 }, { "tag": "Mathematics - Dynamical Systems", "type": 1 }, { "tag": "Quantitative Biology - Quantitative Methods", "type": 1 }, { "tag": "Statistics - Machine Learning", "type": 1 } ], "collections": [ "RBVBDWDI" ], "relations": {}, "dateAdded": "2025-04-22T14:03:07Z", "dateModified": "2025-04-22T14:03:07Z" } }, { "key": "LVP3NYJN", "version": 438, "library": { "type": "group", "id": 362459, "name": "DynElasticNet", "links": { "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/362459/items/LVP3NYJN", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet/items/LVP3NYJN", "type": "text/html" }, "up": { "href": "https://api.zotero.org/groups/362459/items/26ALGRSJ", "type": "application/json" } }, "meta": { "createdByUser": { "id": 1366190, "username": "kschischo", "name": "Maik Kschischo", "links": { "alternate": { "href": "https://www.zotero.org/kschischo", "type": "text/html" } } }, "numChildren": 0 }, "data": { "key": "LVP3NYJN", "version": 438, "parentItem": "26ALGRSJ", "itemType": "attachment", "linkMode": "imported_url", "title": "Full Text PDF", "accessDate": "2025-04-22T13:59:48Z", "url": "https://www.science.org/doi/pdf/10.1126/sciadv.aay2631", "note": "", "contentType": "application/pdf", "charset": "", "filename": "Udrescu and Tegmark - 2020 - AI Feynman A physics-inspired method for symbolic regression.pdf", "md5": "a195d2eb2793453c057f1bc8f34f18cb", "mtime": 1745330388315, "tags": [], "relations": {}, "dateAdded": "2025-04-22T13:59:48Z", "dateModified": "2025-04-22T13:59:48Z" } }, { "key": "26ALGRSJ", "version": 436, "library": { "type": "group", "id": 362459, "name": "DynElasticNet", "links": { "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/362459/items/26ALGRSJ", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet/items/26ALGRSJ", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1366190, "username": "kschischo", "name": "Maik Kschischo", "links": { "alternate": { "href": "https://www.zotero.org/kschischo", "type": "text/html" } } }, "creatorSummary": "Udrescu and Tegmark", "parsedDate": "2020-04-17", "numChildren": 1 }, "data": { "key": "26ALGRSJ", "version": 436, "itemType": "journalArticle", "title": "AI Feynman: A physics-inspired method for symbolic regression", "creators": [ { "creatorType": "author", "firstName": "Silviu-Marian", "lastName": "Udrescu" }, { "creatorType": "author", "firstName": "Max", "lastName": "Tegmark" } ], "abstractNote": "Our physics-inspired algorithm for symbolic regression is able to discover complex physics equations from mere tables of numbers.\n , \n \n A core challenge for both physics and artificial intelligence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of practical interest often exhibit symmetries, separability, compositionality, and other simplifying properties. In this spirit, we develop a recursive multidimensional symbolic regression algorithm that combines neural network fitting with a suite of physics-inspired techniques. We apply it to 100 equations from the\n Feynman Lectures on Physics\n , and it discovers all of them, while previous publicly available software cracks only 71; for a more difficult physics-based test set, we improve the state-of-the-art success rate from 15 to 90%.", "publicationTitle": "Science Advances", "publisher": "", "place": "", "date": "2020-04-17", "volume": "6", "issue": "16", "section": "", "partNumber": "", "partTitle": "", "pages": "eaay2631", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "Sci. Adv.", "DOI": "10.1126/sciadv.aay2631", "citationKey": "", "url": "https://www.science.org/doi/10.1126/sciadv.aay2631", "accessDate": "2025-04-22T13:59:44Z", "PMID": "", "PMCID": "", "ISSN": "2375-2548", "archive": "", "archiveLocation": "", "shortTitle": "AI Feynman", "language": "en", "libraryCatalog": "DOI.org (Crossref)", "callNumber": "", "rights": "", "extra": "", "tags": [], "collections": [ "RBVBDWDI" ], "relations": {}, "dateAdded": "2025-04-22T13:59:44Z", "dateModified": "2025-04-22T13:59:44Z" } }, { "key": "4ZT3EC8W", "version": 435, "library": { "type": "group", "id": 362459, "name": "DynElasticNet", "links": { "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/362459/items/4ZT3EC8W", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet/items/4ZT3EC8W", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1366190, "username": "kschischo", "name": "Maik Kschischo", "links": { "alternate": { "href": "https://www.zotero.org/kschischo", "type": "text/html" } } }, "creatorSummary": "Schmidt and Lipson", "parsedDate": "2009-04-03", "numChildren": 0 }, "data": { "key": "4ZT3EC8W", "version": 435, "itemType": "journalArticle", "title": "Distilling Free-Form Natural Laws from Experimental Data", "creators": [ { "creatorType": "author", "firstName": "Michael", "lastName": "Schmidt" }, { "creatorType": "author", "firstName": "Hod", "lastName": "Lipson" } ], "abstractNote": "For centuries, scientists have attempted to identify and document analytical laws that underlie physical phenomena in nature. Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. A key challenge to finding analytic relations automatically is defining algorithmically what makes a correlation in observed data important and insightful. We propose a principle for the identification of nontriviality. We demonstrated this approach by automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula. Without any prior knowledge about physics, kinematics, or geometry, the algorithm discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation. The discovery rate accelerated as laws found for simpler systems were used to bootstrap explanations for more complex systems, gradually uncovering the “alphabet” used to describe those systems.", "publicationTitle": "Science", "publisher": "", "place": "", "date": "2009-04-03", "volume": "324", "issue": "5923", "section": "", "partNumber": "", "partTitle": "", "pages": "81-85", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "Science", "DOI": "10.1126/science.1165893", "citationKey": "", "url": "https://www.science.org/doi/10.1126/science.1165893", "accessDate": "2025-04-22T13:58:27Z", "PMID": "", "PMCID": "", "ISSN": "0036-8075, 1095-9203", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "en", "libraryCatalog": "DOI.org (Crossref)", "callNumber": "", "rights": "", "extra": "", "tags": [], "collections": [ "RBVBDWDI" ], "relations": {}, "dateAdded": "2025-04-22T13:58:27Z", "dateModified": "2025-04-22T13:58:27Z" } }, { "key": "HSTE7BXR", "version": 469, "library": { "type": "group", "id": 362459, "name": "DynElasticNet", "links": { "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/362459/items/HSTE7BXR", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet/items/HSTE7BXR", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1366190, "username": "kschischo", "name": "Maik Kschischo", "links": { "alternate": { "href": "https://www.zotero.org/kschischo", "type": "text/html" } } }, "creatorSummary": "Korte and Vygen", "parsedDate": "2018", "numChildren": 0 }, "data": { "key": "HSTE7BXR", "version": 469, "itemType": "book", "title": "Combinatorial Optimization: Theory and Algorithms", "creators": [ { "creatorType": "author", "firstName": "Bernhard", "lastName": "Korte" }, { "creatorType": "author", "firstName": "Jens", "lastName": "Vygen" } ], "abstractNote": "", "series": "Algorithms and Combinatorics", "seriesNumber": "", "volume": "21", "numberOfVolumes": "", "edition": "", "date": "2018", "publisher": "Springer Berlin Heidelberg", "place": "Berlin, Heidelberg", "originalDate": "", "originalPublisher": "", "originalPlace": "", "format": "", "numPages": "", "ISBN": "978-3-662-56038-9 978-3-662-56039-6", "DOI": "10.1007/978-3-662-56039-6", "citationKey": "", "url": "https://link.springer.com/10.1007/978-3-662-56039-6", "accessDate": "2025-04-18T15:36:46Z", "ISSN": "", "archive": "", "archiveLocation": "", "shortTitle": "Combinatorial Optimization", "language": "en", "libraryCatalog": "DOI.org (Crossref)", "callNumber": "", "rights": "https://www.springer.com/tdm", "extra": "", "tags": [], "collections": [ "RBVBDWDI" ], "relations": {}, "dateAdded": "2025-04-18T15:36:46Z", "dateModified": "2025-04-18T15:36:46Z" } }, { "key": "WRFBZNNU", "version": 426, "library": { "type": "group", "id": 362459, "name": "DynElasticNet", "links": { "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/362459/items/WRFBZNNU", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet/items/WRFBZNNU", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1366190, "username": "kschischo", "name": "Maik Kschischo", "links": { "alternate": { "href": "https://www.zotero.org/kschischo", "type": "text/html" } } }, "creatorSummary": "Reinthal", "parsedDate": "2020", "numChildren": 0 }, "data": { "key": "WRFBZNNU", "version": 426, "itemType": "thesis", "title": "Extending sparse identification of nonlinear dynamical systems to holonomic dynamical systems", "creators": [ { "creatorType": "author", "firstName": "Vincent", "lastName": "Reinthal" } ], "abstractNote": "", "thesisType": "Master's Thesis", "university": "Universität Bonn", "place": "Department of Computer Science", "date": "2020", "series": "", "seriesNumber": "", "numPages": "", "DOI": "", "ISBN": "", "citationKey": "", "url": "", "accessDate": "", "ISSN": "", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "", "libraryCatalog": "", "callNumber": "", "rights": "", "extra": "", "tags": [], "collections": [ "RBVBDWDI" ], "relations": {}, "dateAdded": "2021-01-27T18:18:17Z", "dateModified": "2021-01-27T18:20:28Z" } }, { "key": "AP6MXQYY", "version": 421, "library": { "type": "group", "id": 362459, "name": "DynElasticNet", "links": { "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/362459/items/AP6MXQYY", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet/items/AP6MXQYY", "type": "text/html" }, "up": { "href": "https://api.zotero.org/groups/362459/items/JNC4EL2F", "type": "application/json" } }, "meta": { "createdByUser": { "id": 1366190, "username": "kschischo", "name": "Maik Kschischo", "links": { "alternate": { "href": "https://www.zotero.org/kschischo", "type": "text/html" } } }, "numChildren": 0 }, "data": { "key": "AP6MXQYY", "version": 421, "parentItem": "JNC4EL2F", "itemType": "attachment", "linkMode": "imported_url", "title": "Full Text", "accessDate": "2021-01-27T17:58:45Z", "url": "https://www.frontiersin.org/articles/10.3389/fphys.2020.612590/pdf", "note": "", "contentType": "application/pdf", "charset": "", "filename": "Kahl and Kschischo - 2021 - Searching for Errors in Models of Complex Dynamic .pdf", "md5": null, "mtime": null, "tags": [], "relations": {}, "dateAdded": "2021-01-27T17:58:45Z", "dateModified": "2021-01-27T17:58:45Z" } }, { "key": "JNC4EL2F", "version": 421, "library": { "type": "group", "id": 362459, "name": "DynElasticNet", "links": { "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/362459/items/JNC4EL2F", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet/items/JNC4EL2F", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1366190, "username": "kschischo", "name": "Maik Kschischo", "links": { "alternate": { "href": "https://www.zotero.org/kschischo", "type": "text/html" } } }, "creatorSummary": "Kahl and Kschischo", "parsedDate": "2021-01-11", "numChildren": 1 }, "data": { "key": "JNC4EL2F", "version": 421, "itemType": "journalArticle", "title": "Searching for Errors in Models of Complex Dynamic Systems", "creators": [ { "creatorType": "author", "firstName": "Dominik", "lastName": "Kahl" }, { "creatorType": "author", "firstName": "Maik", "lastName": "Kschischo" } ], "abstractNote": "Mathematical modeling is seen as a key step to understand, predict, and control the temporal dynamics of interacting systems in such diverse areas like physics, biology, medicine, and economics. However, for large and complex systems we usually have only partial knowledge about the network, the coupling functions, and the interactions with the environment governing the dynamic behavior. This incomplete knowledge induces structural model errors which can in turn be the cause of erroneous model predictions or misguided interpretations. Uncovering the location of such structural model errors in large networks can be a daunting task for a modeler. Here, we present a data driven method to search for structural model errors and to confine their position in large and complex dynamic networks. We introduce a coherence measure for pairs of network nodes, which indicates, how difficult it is to distinguish these nodes as sources of an error. By clustering network nodes into coherence groups and inferring the cluster inputs we can decide, which cluster is affected by an error. We demonstrate the utility of our method for the\n C. elegans\n neural network, for a signal transduction model for UV-B light induced morphogenesis and for synthetic examples.", "publicationTitle": "Frontiers in Physiology", "publisher": "", "place": "", "date": "2021-1-11", "volume": "11", "issue": "", "section": "", "partNumber": "", "partTitle": "", "pages": "612590", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "Front. Physiol.", "DOI": "10.3389/fphys.2020.612590", "citationKey": "", "url": "https://www.frontiersin.org/articles/10.3389/fphys.2020.612590/full", "accessDate": "2021-01-27T17:58:43Z", "PMID": "", "PMCID": "", "ISSN": "1664-042X", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "", "libraryCatalog": "DOI.org (Crossref)", "callNumber": "", "rights": "", "extra": "", "tags": [], "collections": [ "RBVBDWDI" ], "relations": {}, "dateAdded": "2021-01-27T17:58:43Z", "dateModified": "2021-01-27T17:58:43Z" } }, { "key": "CF7FKQFS", "version": 415, "library": { "type": "group", "id": 362459, "name": "DynElasticNet", "links": { "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/362459/items/CF7FKQFS", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet/items/CF7FKQFS", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1366190, "username": "kschischo", "name": "Maik Kschischo", "links": { "alternate": { "href": "https://www.zotero.org/kschischo", "type": "text/html" } } }, "creatorSummary": "Newmiwaka et al.", "parsedDate": "2020-09-15", "numChildren": 0 }, "data": { "key": "CF7FKQFS", "version": 415, "itemType": "journalArticle", "title": "SEEDS: data driven inference of structural model errors and unknown inputs for dynamic systems biology", "creators": [ { "creatorType": "author", "firstName": "Tobias", "lastName": "Newmiwaka" }, { "creatorType": "author", "firstName": "Benjamin", "lastName": "Engelhardt" }, { "creatorType": "author", "firstName": "Philipp", "lastName": "Wendland" }, { "creatorType": "author", "firstName": "Dominik", "lastName": "Kahl" }, { "creatorType": "author", "firstName": "Holger", "lastName": "Fröhlich" }, { "creatorType": "author", "firstName": "Maik", "lastName": "Kschischo" }, { "creatorType": "editor", "firstName": "Martelli", "lastName": "Pier Luigi" } ], "abstractNote": "Abstract\n \n Summary\n Dynamic models formulated as ordinary differential equations can provide information about the mechanistic and causal interactions in biological systems to guide targeted interventions and to design further experiments. Inaccurate knowledge about the structure, functional form and parameters of interactions is a major obstacle to mechanistic modeling. A further challenge is the open nature of biological systems which receive unknown inputs from their environment. The R-package SEEDS implements two recently developed algorithms to infer structural model errors and unknown inputs from output measurements. This information can facilitate efficient model recalibration as well as experimental design in the case of misfits between the initial model and data.\n \n \n Availability and implementation\n For the R-package seeds, see the CRAN server https://cran.r-project.org/package=seeds.", "publicationTitle": "Bioinformatics", "publisher": "", "place": "", "date": "2020-09-15", "volume": "", "issue": "", "section": "", "partNumber": "", "partTitle": "", "pages": "btaa786", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "", "DOI": "10.1093/bioinformatics/btaa786", "citationKey": "", "url": "https://academic.oup.com/bioinformatics/advance-article/doi/10.1093/bioinformatics/btaa786/5906024", "accessDate": "2021-01-27T17:26:11Z", "PMID": "", "PMCID": "", "ISSN": "1367-4803, 1460-2059", "archive": "", "archiveLocation": "", "shortTitle": "SEEDS", "language": "en", "libraryCatalog": "DOI.org (Crossref)", "callNumber": "", "rights": "", "extra": "", "tags": [], "collections": [ "RBVBDWDI" ], "relations": {}, "dateAdded": "2021-01-27T17:26:11Z", "dateModified": "2021-01-27T17:26:11Z" } }, { "key": "JD432IF3", "version": 413, "library": { "type": "group", "id": 362459, "name": "DynElasticNet", "links": { "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/362459/items/JD432IF3", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet/items/JD432IF3", "type": "text/html" }, "up": { "href": "https://api.zotero.org/groups/362459/items/49RWH77U", "type": "application/json" } }, "meta": { "createdByUser": { "id": 1366190, "username": "kschischo", "name": "Maik Kschischo", "links": { "alternate": { "href": "https://www.zotero.org/kschischo", "type": "text/html" } } }, "numChildren": 0 }, "data": { "key": "JD432IF3", "version": 413, "parentItem": "49RWH77U", "itemType": "attachment", "linkMode": "imported_url", "title": "Full Text", "accessDate": "2020-11-27T19:43:03Z", "url": "https://royalsocietypublishing.org/doi/pdf/10.1098/rsif.2019.0043", "note": "", "contentType": "application/pdf", "charset": "", "filename": "Villaverde et al. - 2019 - Full observability and estimation of unknown input.pdf", "md5": null, "mtime": null, "tags": [], "relations": {}, "dateAdded": "2020-11-27T19:43:03Z", "dateModified": "2020-11-27T19:43:03Z" } }, { "key": "49RWH77U", "version": 413, "library": { "type": "group", "id": 362459, "name": "DynElasticNet", "links": { "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/362459/items/49RWH77U", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet/items/49RWH77U", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1366190, "username": "kschischo", "name": "Maik Kschischo", "links": { "alternate": { "href": "https://www.zotero.org/kschischo", "type": "text/html" } } }, "creatorSummary": "Villaverde et al.", "parsedDate": "2019", "numChildren": 1 }, "data": { "key": "49RWH77U", "version": 413, "itemType": "journalArticle", "title": "Full observability and estimation of unknown inputs, states and parameters of nonlinear biological models", "creators": [ { "creatorType": "author", "firstName": "Alejandro F.", "lastName": "Villaverde" }, { "creatorType": "author", "firstName": "Nikolaos", "lastName": "Tsiantis" }, { "creatorType": "author", "firstName": "Julio R.", "lastName": "Banga" } ], "abstractNote": "In this paper, we address the system identification problem in the context of biological modelling. We present and demonstrate a methodology for (i) assessing the possibility of inferring the unknown quantities in a dynamic model and (ii) effectively estimating them from output data. We introduce the term Full Input-State-Parameter Observability (FISPO) analysis to refer to the simultaneous assessment of state, input and parameter observability (note that parameter observability is also known as identifiability). This type of analysis has often remained elusive in the presence of unmeasured inputs. The method proposed in this paper can be applied to a general class of nonlinear ordinary differential equations models. We apply this approach to three models from the recent literature. First, we determine whether it is theoretically possible to infer the states, parameters and inputs, taking only the model equations into account. When this analysis detects deficiencies, we reformulate the model to make it fully observable. Then we move to numerical scenarios and apply an optimization-based technique to estimate the states, parameters and inputs. The results demonstrate the feasibility of an integrated strategy for (i) analysing the theoretical possibility of determining the states, parameters and inputs to a system and (ii) solving the practical problem of actually estimating their values.", "publicationTitle": "Journal of The Royal Society Interface", "publisher": "", "place": "", "date": "07/2019", "volume": "16", "issue": "156", "section": "", "partNumber": "", "partTitle": "", "pages": "20190043", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "J. R. Soc. Interface.", "DOI": "10.1098/rsif.2019.0043", "citationKey": "", "url": "https://royalsocietypublishing.org/doi/10.1098/rsif.2019.0043", "accessDate": "2020-11-27T19:43:01Z", "PMID": "", "PMCID": "", "ISSN": "1742-5689, 1742-5662", "archive": "", "archiveLocation": "", "shortTitle": "", "language": "en", "libraryCatalog": "DOI.org (Crossref)", "callNumber": "", "rights": "", "extra": "", "tags": [], "collections": [], "relations": {}, "dateAdded": "2020-11-27T19:43:01Z", "dateModified": "2020-11-27T19:43:01Z" } }, { "key": "48JHDKWI", "version": 412, "library": { "type": "group", "id": 362459, "name": "DynElasticNet", "links": { "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet", "type": "text/html" } } }, "links": { "self": { "href": "https://api.zotero.org/groups/362459/items/48JHDKWI", "type": "application/json" }, "alternate": { "href": "https://www.zotero.org/groups/dynelasticnet/items/48JHDKWI", "type": "text/html" } }, "meta": { "createdByUser": { "id": 1366190, "username": "kschischo", "name": "Maik Kschischo", "links": { "alternate": { "href": "https://www.zotero.org/kschischo", "type": "text/html" } } }, "creatorSummary": "Honerkamp and Weese", "parsedDate": "1990", "numChildren": 0 }, "data": { "key": "48JHDKWI", "version": 412, "itemType": "journalArticle", "title": "Tikhonovs regularization method for ill-posed problems: A comparison of different methods for the determination of the regularization parameter", "creators": [ { "creatorType": "author", "firstName": "J.", "lastName": "Honerkamp" }, { "creatorType": "author", "firstName": "J.", "lastName": "Weese" } ], "abstractNote": "", "publicationTitle": "Continuum Mechanics and Thermodynamics", "publisher": "", "place": "", "date": "1990", "volume": "2", "issue": "1", "section": "", "partNumber": "", "partTitle": "", "pages": "17-30", "series": "", "seriesTitle": "", "seriesText": "", "journalAbbreviation": "Continuum Mech. Thermodyn", "DOI": "10.1007/BF01170953", "citationKey": "", "url": "http://link.springer.com/10.1007/BF01170953", "accessDate": "2020-11-27T17:47:35Z", "PMID": "", "PMCID": "", "ISSN": "0935-1175, 1432-0959", "archive": "", "archiveLocation": "", "shortTitle": "Tikhonovs regularization method for ill-posed problems", "language": "en", "libraryCatalog": "DOI.org (Crossref)", "callNumber": "", "rights": "", "extra": "", "tags": [], "collections": [], "relations": {}, "dateAdded": "2020-11-27T17:47:35Z", "dateModified": "2020-11-27T17:47:35Z" } } ]