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They provide a nonnumerical pathway to solving partial differential equations by expressing the field solution as an artificial neural network. This approach has been applied successfully to various types of differential equations. A major area of research on PINNs is the application to coupled partial differential equations in particular, and a general breakthrough is still lacking. In coupled equations, the optimization operates in a critical conflict between boundary conditions and the underlying equations, which often requires either many iterations or complex schemes to avoid trivial solutions and to achieve convergence. We provide empirical evidence for the mitigation of bad initial conditioning in PINNs for solving one-dimensional consolidation problems of porous media through the introduction of affine transformations after the classical output layer of artificial neural network architectures, effectively accelerating the training process. These affine physics-informed neural networks~(AfPINNs) then produce nontrivial and accurate field solutions even in parameter spaces with diverging orders of magnitude. On average, AfPINNs show the ability to improve the [Formula: see text] relative error by [Formula: see text] after 25,000 epochs for a one-dimensional consolidation problem based on Biot's theory, and an average improvement by [Formula: see text] with a transfer approach to the theory of porous media.", "file" : "Mandl, Mielke et al. 2023 - Affine transformations accelerate the training:Attachments/Mandl, Mielke et al. 2023 - Affine transformations accelerate the training.pdf:application/pdf", "doi" : "10.1038/s41598-023-42141-x", "bibtexKey": "Mandl.2023" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/23d4f476ebe3785666ff01ad58f9b878a/simtech", "tags" : [ "PN2-2A","PN2","curated","PN2-2(II)","EXC2075" ], "intraHash" : "3d4f476ebe3785666ff01ad58f9b878a", "interHash" : "173fb49a1dcdfa9efd0f172ba03cce80", "label" : "Non-local three phase lag bio thermal modeling of skin tissue and experimental evaluation", "user" : "simtech", "description" : "", "date" : "2023-11-15 18:11:17", "changeDate" : "2024-06-06 16:21:12", "count" : 9, "pub-type": "article", "journal": "International Communications in Heat and Mass Transfer", "year": "2023", "url": "https://www.sciencedirect.com/science/article/pii/S0735193323005353", "author": [ "Mohammad Azhdari","Seyed Morteza Seyedpour","Lena Lambers","Hans-Michael Tautenhahn","Franziska Tautenhahn","Tim Ricken","Ghader Rezazadeh" ], "authors": [ {"first" : "Mohammad", "last" : "Azhdari"}, {"first" : "Seyed Morteza", "last" : "Seyedpour"}, {"first" : "Lena", "last" : "Lambers"}, {"first" : "Hans-Michael", "last" : "Tautenhahn"}, {"first" : "Franziska", "last" : "Tautenhahn"}, {"first" : "Tim", "last" : "Ricken"}, {"first" : "Ghader", "last" : "Rezazadeh"} ], "volume": "149","pages": "107146","abstract": "In this paper, the thermal behavior of living tissue has been modeled using a non-local three-phase lag approach. The simulation results of this model- ing have been compared with experimental results of alternating radiation with different periods on human skin, yielding satisfactory alignments. Ad- ditionally, it has been investigated that the TPL model, which is an equation with an integral term, can simulate energy accumulation within the dermal tissue. Moreover, the non-local nature of the modeling has been explored to alter the influence of phase lag terms. Furthermore, apart from numer- ically solving the equation, an analytical solution has been derived for the frequency equation, demonstrating the effects of simulation parameters on the frequency equation and simulation results. The obtained results indi cate that these parameters not only independently affect the outcomes but also interact with other parameters, leading to variations beyond their direct impacts.", "issn" : "0735-1933", "doi" : "https://doi.org/10.1016/j.icheatmasstransfer.2023.107146", "bibtexKey": "AZHDARI2023107146" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/223851cd356770672ee824c3fbac337da/simtech", "tags" : [ "EXC2075","PN2","PN2-2A","curated" ], "intraHash" : "23851cd356770672ee824c3fbac337da", "interHash" : "c962660da154f21f7b3abcd27353df88", "label" : "Simulation of Contaminant Transport through the Vadose Zone: A Continuum Mechanical Approach within the Framework of the Extended Theory of Porous Media (eTPM)", "user" : "simtech", "description" : "", "date" : "2023-11-15 18:07:04", "changeDate" : "2023-12-06 08:55:18", "count" : 7, "pub-type": "article", "journal": "Water", "year": "2023", "url": "https://www.mdpi.com/2073-4441/15/2/343", "author": [ "S. M. Seyedpour","A. Thom","T. Ricken" ], "authors": [ {"first" : "S. M.", "last" : "Seyedpour"}, {"first" : "A.", "last" : "Thom"}, {"first" : "T.", "last" : "Ricken"} ], "volume": "15","number": "2","abstract": "The simulation of contaminant transport through the vadose zone enjoys high significance for decision makers and contaminated site planners since the vadose zone can serve as a filter, but many contaminants can be transported from this region to aquifers. The intention of this paper is to utilize the extended Theory of Porous Media (eTPM) to develop a ternary model for the simulation of contaminant transport in the vadose zone whose application is subsequently shown via a numerical example. The simulation was conducted for 140 days, during which the contamination source was removed after 25 days. The results indicate that the contaminant reached the water table after 76 days. The concentration of the contaminant reaching the groundwater was 17% less than that of the contaminant source.", "issn" : "2073-4441", "article-number" : "343", "doi" : "10.3390/w15020343", "bibtexKey": "w15020343" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2517e881ebc7038da8aa5d1a140340091/simtech", "tags" : [ "EXC2075","PN2","PN2-2A","curated" ], "intraHash" : "517e881ebc7038da8aa5d1a140340091", "interHash" : "975bd483b966118833f2d39f99338688", "label" : "On robust discretization methods for poroelastic problems: Numerical examples and counter-examples", "user" : "simtech", "description" : "", "date" : "2023-11-15 18:06:07", "changeDate" : "2023-12-06 08:55:18", "count" : 7, "pub-type": "article", "journal": "Examples and Counterexamples","publisher":"Elsevier BV", "year": "2022", "url": "http://dx.doi.org/10.1016/j.exco.2022.100087", "author": [ "Fleurianne Bertrand","Maximilian Brodbeck","Tim Ricken" ], "authors": [ {"first" : "Fleurianne", "last" : "Bertrand"}, {"first" : "Maximilian", "last" : "Brodbeck"}, {"first" : "Tim", "last" : "Ricken"} ], "volume": "2","pages": "100087", "issn" : "2666-657X", "doi" : "10.1016/j.exco.2022.100087", "bibtexKey": "Bertrand_2022" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/23a9df66447921dfe31d3723c1d8901a3/simtech", "tags" : [ "PN2-2A","PN2","curated","EXC2075" ], "intraHash" : "3a9df66447921dfe31d3723c1d8901a3", "interHash" : "e158a3480455513ffb6b087efe708b27", "label" : "Semi-automated Data-driven FE Mesh Generation and Inverse Parameter Identification for a Multiscale and Multiphase Model of Function-Perfusion Processes in the Liver", "user" : "simtech", "description" : "", "date" : "2021-12-15 09:47:36", "changeDate" : "2024-06-06 16:22:00", "count" : 9, "pub-type": "article", "journal": "PAMM", "year": "2021", "url": "", "author": [ "Lena Lambers","André Mielke","Tim Ricken" ], "authors": [ {"first" : "Lena", "last" : "Lambers"}, {"first" : "André", "last" : "Mielke"}, {"first" : "Tim", "last" : "Ricken"} ], "volume": "21","number": "1", "issn" : "1617-7061", "doi" : "10.1002/pamm.202100190", "bibtexKey": "Lambers.2021" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/201a9d22b6f3646d3a3d7210f346db251/simtech", "tags" : [ "EXC2075","PN2","PN2-2A","curated" ], "intraHash" : "01a9d22b6f3646d3a3d7210f346db251", "interHash" : "2767cc050e2473714b929359f37201f6", "label" : "Optimization of the Groundwater Remediation Process Using a Coupled Genetic Algorithm-Finite Difference Method", "user" : "simtech", "description" : "", "date" : "2021-12-08 15:09:37", "changeDate" : "2023-12-06 08:55:18", "count" : 9, "pub-type": "article", "journal": "Water", "year": "2021", "url": "", "author": [ "S. M. Seyedpour","I. Valizadeh","P. Kirmizakis","R. Doherty","T. Ricken" ], "authors": [ {"first" : "S. M.", "last" : "Seyedpour"}, {"first" : "I.", "last" : "Valizadeh"}, {"first" : "P.", "last" : "Kirmizakis"}, {"first" : "R.", "last" : "Doherty"}, {"first" : "T.", "last" : "Ricken"} ], "volume": "13","number": "3","pages": "383", "file" : "Das Attachment konnte nicht verknüpft werden. Die interne Fehlermeldung lautet: Eine Ausnahme vom Typ \"SwissAcademic.Azure.CitaviWebApiException\" wurde ausgelöst.", "doi" : "10.3390/w13030383", "bibtexKey": "Seyedpour.2021" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/206221325d59bb950978bf1af0b87f101/simtech", "tags" : [ "PN2-2A","PN2","curated","EXC2075" ], "intraHash" : "06221325d59bb950978bf1af0b87f101", "interHash" : "3df8d34d150827c5a06fbf4aad65e873", "label" : "Model Order Reduction (MOR) of Function--Perfusion--Growth Simulation in the Human Fatty Liver via Artificial Neural Network (ANN)", "user" : "simtech", "description" : "", "date" : "2021-12-08 10:22:11", "changeDate" : "2024-06-06 16:28:12", "count" : 6, "pub-type": "article", "journal": "PAMM", "year": "2019", "url": "", "author": [ "Lena Lambers","Tim Ricken","Matthias König" ], "authors": [ {"first" : "Lena", "last" : "Lambers"}, {"first" : "Tim", "last" : "Ricken"}, {"first" : "Matthias", "last" : "König"} ], "volume": "19","number": "1", "issn" : "1617-7061", "doi" : "10.1002/pamm.201900429", "bibtexKey": "Lambers.2019" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/282b1dca30b5186cfac1a7632c81268a1/simtech", "tags" : [ "PN2-2A","PN2","curated","EXC2075" ], "intraHash" : "82b1dca30b5186cfac1a7632c81268a1", "interHash" : "835491832a8cfd63910d9978944c7e0a", "label" : "A Multiscale and Multiphase Model of Function-Perfusion Growth Processes in the Human Liver", "user" : "simtech", "description" : "", "date" : "2021-12-08 10:21:11", "changeDate" : "2024-06-06 16:27:23", "count" : 12, "pub-type": "article", "journal": "PAMM","publisher":"Wiley", "year": "2021", "url": "https://doi.org/10.1002%2Fpamm.202000290", "author": [ "Lena Lambers","Marlon Suditsch","Arndt Wagner","Tim Ricken" ], "authors": [ {"first" : "Lena", "last" : "Lambers"}, {"first" : "Marlon", "last" : "Suditsch"}, {"first" : "Arndt", "last" : "Wagner"}, {"first" : "Tim", "last" : "Ricken"} ], "volume": "20","number": "1", "doi" : "10.1002/pamm.202000290", "bibtexKey": "Lambers_2021" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/21daa67ebcaa8cad33fd93ca56887731f/simtech", "tags" : [ "PN2-2A","PN2","curated","EXC2075" ], "intraHash" : "1daa67ebcaa8cad33fd93ca56887731f", "interHash" : "121191d43d6f35724b8721c8e15f0329", "label" : "Least Squares Finite Element Method for Hepatic Sinusoidal Blood Flow", "user" : "simtech", "description" : "", "date" : "2021-12-08 10:20:25", "changeDate" : "2024-06-06 16:27:42", "count" : 8, "pub-type": "article", "journal": "PAMM","publisher":"Wiley", "year": "2021", "url": "https://doi.org/10.1002%2Fpamm.202000306", "author": [ "Fleurianne Bertrand","Lena Lambers","Tim Ricken" ], "authors": [ {"first" : "Fleurianne", "last" : "Bertrand"}, {"first" : "Lena", "last" : "Lambers"}, {"first" : "Tim", "last" : "Ricken"} ], "volume": "20","number": "1", "doi" : "10.1002/pamm.202000306", "bibtexKey": "Bertrand_2021" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2f539da2c8354ef34f26ae34bd8371aef/simtech", "tags" : [ "PN2-2A","PN2","curated","EXC2075" ], "intraHash" : "f539da2c8354ef34f26ae34bd8371aef", "interHash" : "4d72b7eff2282d9ac8dec12295b4c5f3", "label" : "Modelling basal-cell carcinoma behaviour in avascular skin", "user" : "simtech", "description" : "", "date" : "2021-12-08 10:16:50", "changeDate" : "2024-06-06 16:27:04", "count" : 9, "pub-type": "article", "journal": "PAMM","publisher":"Wiley", "year": "2021", "url": "https://doi.org/10.1002%2Fpamm.202000283", "author": [ "M. Suditsch","P. Schröder","L. Lambers","T. Ricken","W. Ehlers","A. Wagner" ], "authors": [ {"first" : "M.", "last" : "Suditsch"}, {"first" : "P.", "last" : "Schröder"}, {"first" : "L.", "last" : "Lambers"}, {"first" : "T.", "last" : "Ricken"}, {"first" : "W.", "last" : "Ehlers"}, {"first" : "A.", "last" : "Wagner"} ], "volume": "20","number": "1", "doi" : "10.1002/pamm.202000283", "bibtexKey": "Suditsch_2021" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/28ed524c52e8b0a1e38ea86022b3f0371/simtech", "tags" : [ "PN2-2A","EXC2075","PN2","curated" ], "intraHash" : "8ed524c52e8b0a1e38ea86022b3f0371", "interHash" : "78bfefeec024e06c4b62132c4c4b6af3", "label" : "Application of Magnetic Resonance Imaging in Liver Biomechanics: A Systematic Review", "user" : "simtech", "description" : "", "date" : "2021-12-08 10:09:48", "changeDate" : "2024-06-06 16:26:47", "count" : 8, "pub-type": "article", "journal": "Frontiers in Physiology","publisher":"Frontiers Media SA", "year": "2021", "url": "https://doi.org/10.3389%2Ffphys.2021.733393", "author": [ "Seyed M. 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Reichenbach","Tim Ricken" ], "authors": [ {"first" : "Seyed M.", "last" : "Seyedpour"}, {"first" : "Mehdi", "last" : "Nabati"}, {"first" : "Lena", "last" : "Lambers"}, {"first" : "Sara", "last" : "Nafisi"}, {"first" : "Hans-Michael", "last" : "Tautenhahn"}, {"first" : "Ingolf", "last" : "Sack"}, {"first" : "Jürgen R.", "last" : "Reichenbach"}, {"first" : "Tim", "last" : "Ricken"} ], "volume": "12", "doi" : "10.3389/fphys.2021.733393", "bibtexKey": "Seyedpour_2021" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/28fb1c1d1d7399358323ccb8a39f3bf03/simtech", "tags" : [ "PN2-2A","EXC2075","PN2","curated" ], "intraHash" : "8fb1c1d1d7399358323ccb8a39f3bf03", "interHash" : "f91b6da0dac73038da67f3ce8aeb2f21", "label" : "Hepatectomy-Induced Alterations in Hepatic Perfusion and Function - Toward Multi-Scale Computational Modeling for a Better Prediction of Post-hepatectomy Liver Function", "user" : "simtech", "description" : "", "date" : "2021-12-08 09:58:09", "changeDate" : "2024-06-06 16:26:21", "count" : 8, "pub-type": "article", "journal": "Frontiers in Physiology","publisher":"Frontiers Media SA", "year": "2021", "url": "https://doi.org/10.3389%2Ffphys.2021.733868", "author": [ "Bruno Christ","Maximilian Collatz","Uta Dahmen","Karl-Heinz Herrmann","Sebastian Höpfl","Matthias König","Lena Lambers","Manja Marz","Daria Meyer","Nicole Radde","Jürgen R. 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