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[PDE & Applications seminar] Sebastian Wieczorek: Rate-induced tipping in non-autonomous reaction-diffusion systems: An invariant manifold framework and shifting habitats

The mathematical modelling of tipping points - large and sudden changes in the state of a system that arise in response to small and slow changes in the external inputs - has mainly focused on ordinary differential equation (ODE) models. In this talk, I will begin with a brief overview of tipping points in ODEs. I will then consider reaction-diffusion equations (RDEs) with time-dependent (nonautonomous) and space-dependent (heterogenous) reaction terms that decay in space (asymptotically homogeneous). Such models are likely to exhibit new and interesting tipping mechanisms, but their analysis is more challenging and requires new techniques. As an illustrative example, we analyse a conceptual model of a habitat patch in one spatial dimension, that features an Allee effect in population growth and is geographically shrinking or shifting due to human activity and climate change. We identify two classes of tipping points to extinction: bifurcation-induced tipping (B-tipping) when the shrinking habitat falls below some critical length, and rate-induced tipping (R-tipping) when the shifting habitat exceeds some critical speed. To facilitate the analysis of tipping points in RDEs, such as the moving habitat model, we propose a new mathematical framework. This framework is underpinned by a special compactification of the moving-frame coordinate in conjunction with Lin’s method for constructing heteroclinic orbits along intersections of stable and unstable invariant manifolds of saddles. This allows us to (i) obtain multiple coexisting pulse and front solutions for the RDE by computing heteroclinic orbits connecting saddles from negative and positive infinity, (ii) detect tipping points as bifurcations of such heteroclinic orbits, and (iii) obtain two-parameter tipping diagrams by numerical continuation of such bifurcations.

Publications

Publications Conferences Jochen Cremer Journals [14] Bastien Giraud, Ali Rajaei, Jochen L. Cremer “Constraint-Driven Deep Learning for N-k Security Constrained Optimal Power Flow”, Electric Power System Research and 2024 IEEE Power System Computation Conference [13] Nikolina Covic, Jochen L. Cremer , Hrvoje Pandžić, “Learning a Reward Function for Optimal Appliance Scheduling” Electric Power System Research and 2024 IEEE Power System Computation Conference arxiv.org/pdf/2310.07389.pdf [12] Charles Renshaw-Whitman, Viktor Zobernig, Jochen L. Cremer , Laurens de Vries, ”The Non-Stationary for Multiagent Reinforcement Learning in Electricity Markets”, Electric Power System Research and 2024 IEEE Power System Computation Conference [11] Al-Amin Bugaje, Jochen L. Cremer , Goran Strbac ”Generating Quality Datasets for Real-Time Security Assessment: Balancing Historically Relevant and Rare Feasible Operating Condition” International Journal of Electrical Power & Energy Systems, 2023 [10] B. Habib, E. Isufi, W. v. Breda, A. Jongepier and Jochen L. Cremer , ”Deep Statistical Solver for Distribution System State Estimation, ” IEEE Transactions on Power Systems, 2023, doi: 10.1109/TPWRS.2023.3290358. [9] Dariush Wahdany, Carlo Schmitt, Jochen L. Cremer , ”More than Accuracy: End-To-End Wind Power Forecasting that Optimises the Energy System”, Electric Power System Research, 2023 [8] Nidarshan Veera Kumar, Jochen L. Cremer , Marjan Popov, ”Incremental learning for real-time electrical disturbance event recognition”, International Journal of Electrical Power & Energy Systems, 2023, (108988) [7] Al-Amin Bugaje, Jochen L. Cremer , Goran Strbac, “Real-time Transmission Switching with Neural Networks” IET Generation, Transmission & Distribution, 2022 [6] Al-Amin Bugaje, Jochen L. Cremer , Goran Strbac, “Split-based Sequential Sampling for Realtime Security Assessment”, International Journal of Electrical Power & Energy Systems, 2022 [5] Federica Bellizio, Jochen L. Cremer , Goran Strbac, ”Transient Stable Corrective Control in Smart Grids Using Neural Lyapunov Learning”, IEEE Transactions of Power Systems, 2022 [4] Antoine Marot, Benjamin Donnot, Karim Chaouache, Adrian Kelly, Qiuhua Huang, Ramij-Raja Hossain, and Jochen L. Cremer . ”Learning to run a power network with trust.” arXiv preprint arXiv:2110.12908. Electric Power Systems Research, 2022 [3] Antoine Marot, Adrian Kelly, Matija Naglic, Vincent Barbesant, Jochen Cremer , Alexandru Stefanov and Jan Viebahn, ”Perspectives for Future Power System Control Centers for The Energy Transition”, IEEE Journal of Modern Power Systems and Clean Energy, 2022 [2] Federica Bellizio, Wangkun Zu, Dawei Qiu, Yujian Ye, Dimitrios Papadaskapoulos, Jochen L. Cremer , Fei Teng, Goran Strbac, “Transition to secure data-driven grid control and decentralized electricity market”, IEEE Proceedings, Special Issue "The Evolution of Smart Grids", 2022 [1] Federica Bellizio, Al-Amin B. Bugaje, Jochen L. Cremer , Goran Strbac, “Verifying Machine Learning Conclusions for Securing Low Inertia Systems”, Sustainable Energy, Grids and Networks, 2022 Peyman Mohajerin Esfahani Journals [11] Jingwei Dong, Arman Sharifi Kolarijani, and Peyman Mohajerin Esfahani , “ Diagnosis for Switched Affine Systems with noisy Measurement ”, Automatica, 2023 [10] Pedro Zattoni Scroccaro, Arman Sharifi Kolarijani, and Peyman Mohajerin Esfahani , “ Adaptive Online Optimization with Predictions: Static and Dynamic Environments ”, IEEE Transactions on Automatic Control, 2023 [9] V. A. Nguyen, S. Shafieezadeh-Abadeh, D. Kuhn, and P. Mohajerin Esfahani , “Bridging Bayesian and Minimax Mean Square Error Estimation via Wasserstein Distributionally Robust Optimization”, Mathematics of Operations Research , 2022 [8] M. Saeed Sarafraz, A. Proskurnikov, M. S. Tavazoei, and P. Mohajerin Esfahani , “Robust Output Regulation: Optimization-Based Synthesis and Event-Triggered Implementation”, IEEE Transactions on Automatic Control , 2022 [7] C. van der Ploeg, E. Silvas, N. v. de Wouw, and P. Mohajerin Esfahani , “Real-time Fault Estimation for a Class of Discrete-Time Linear Parameter-Varying Systems”, IEEE Control Systems Letters , vol. 6, pp. 1988 - 1993, 2021 [6] K. Pan, P. Palensky, and P. Mohajerin Esfahani , “Dynamic Anomaly Detection with High-fidelity Simulators: A Convex Optimization Approach”, IEEE Transactions on Smart Grid , vol. 13, no. 2, pp. 1500-1515, 2022 [5] S. A. Akhtar, A. S. Kolarijani and P. Mohajerin Esfahani , “Learning for Control: An Inverse Optimization Approach”, IEEE Control Systems Letters , vol. 6, pp. 187-192, 2021 [4] B. Gravell, P. Mohajerin Esfahani , and T. Summers, “Learning Robust Controllers for Linear Quadratic Systems with Multiplicative Noise via Policy Gradient”, IEEE Transactions on Automatic Control , vol. 66, no. 11, pp. 5283-5298, 2021 [3] B. V. Parys, P. Mohajerin Esfahani , and D. Kuhn, “From Data to Decisions: Distributionally Robust Optimization is Optimal”, Management Science , vol. 67, no. 6, pp. 3387-3402, 2021 [2] A. Kolarijani, A. Proskurnikov, and P. Mohajerin Esfahani , “Macroscopic Noisy Bounded Confidence Models with Distributed Radical Opinions” IEEE Transactions on Automatic Control , vol. 66, no. 3, pp. 1174-1189, 2021 [1] V. Nguyen, D. Kuhn, and P. Mohajerin Esfahani , “Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator”, Operations Research (OR), vol. 70, no. 1, pp. 490-515, 2021 Conference Abstracts & Proceedings [3] A. Kolarijani, G. Max, and P. Mohajerin Esfahan i, “Fast Approximate Dynamic Programming for Infinite-Horizon Continuous-State Markov Decision Processes”, Neural Information Processing Systems (NeurIPS) , December 2021 [2] R. Vreugdenhil, V. A. Nguyen, A. Eftekhari, P. Mohajerin Esfahani , “Principal Component Hierarchy for Sparse Quadratic Programs”, International Conference on Machine Learning (ICML) , Vienna, Austria, July 2021 [1] J. Dong, A. Sharifi Kolarijani, and P. Mohajerin Esfahani , “Multimode Diagnosis for Switched Affine Systems”, American Control Conference (ACC) , New Orleans, USA, May 2021 This content is being blocked for you because it contains cookies. Would you like to view this content? By clicking here , you will automatically allow the use of cookies.

People

People working at SEE Calling from outside the TU Delft: dial +31-(0)15 27 + the listed number. Email address secretariat: m.h.n.vanvliet@tudelft.nl Academic staff prof.dr.ir. M. Wagemaker (Marnix) +31 (0)15 2783800 m.wagemaker@tudelft.nl Room: 2.01.030 dr. E.M. Kelder (Erik) +31 (0)15 2783262 e.m.kelder@tudelft.nl Room: 2.01.040 dr. ir. L.J. Bannenberg (Lars) +31 (0)15 2789753 l.j.bannenberg@tudelft.nl Room: 2.01.220 dr. S. Ganapathy (Swapna) +31 (0)15 2784533 s.ganapathy@tudelft.nl Room: 2.01.160 Publications ( Google Scholar ) dr. X. Wang (Xuehang) +31 (0)15 2786864 x.wang-22@tudelft.nl Room: 2.01.070 Publication (Google Scholar) Researcher P. Karanth (Pranav) +31 (0)15 2784758 P.Karanth@tudelft.nl Room: 2.01.050 Support staff M.H.N. van Vliet (Martine) +31 (0)15 2782995 m.h.n.vanvliet@tudelft.nl Room: 2.01.290 or 2.01.010 N.S. Ilavazhakan (Nirmal) n.s.ilavazhakan@tudelft.nl Room: 2.01.280 D. Luo (Dan) d.luo-2@tudelft.nl Room: 2.01.280 K. Rajic-Miskovic (Katarina) k.rajic-miskovic@tudelft.nl Room: 2.01.280 F.G.B. Ooms (Frans) +31 (0)15 2783656 f.g.b.ooms@tudelft.nl Room: 2.01.160 M.P. Steenvoorden (Michel) 83189 m.p.steenvoorden@tudelft.nl Room: 2.01.400 Postdocs J. Canals-Riclot (Jef) +31 (0)15 2783021 j.canals-riclot@tudelft.nl Room: 2.01.190 Z. Cheng (Zhu) +31 (0)15 2784758 Z.Cheng@tudelft.nl Room: 2.01.050 H.S. Dewi (Sandra) H.S.HandikaSandraDewi@tudelft.nl A. Gautam (Ajay) +31 (0)15 2784745 A.AjayGautam@tudelft.nl Room: 2.01.080 L. Huet (Lucas) +31 (0)15 2783021 l.q.bikker@student.tudelft.nl Room: 2.01.190 M. Mohan Kumar Sreelatha (Meera) +31 (0)15 27 83021 m.mohankumarsreelatha@tudelft.nl Room: 2.01.190 A. Vasileiadis (Alexandros) +31 (0)15 2784745 a.vasileiadis@tudelft.nl Room: 2.01.080 Q. Wang (Qidi) +31 (0)15 2785574 Q.Wang-11@tudelft.nl Room: 2.01.170 C. Zhao (Chenglong) +31 (0)15 2784745 C.Zhao-1@tudelft.nl Room: 2.01.080 PhD’s H.A.A. Al-Kutubi (Hanan) +31 (0)15 2784758 H.A.A.Al-Kutubi@tudelft.nl Room: 2.01.050 Berg, P.J.L. van den (Peter) +31 (0)15 2784758 P.J.L.vandenBerg@tudelft.nl Room: 2.01.050 Biffo, A.O. (Abdulkadir) +31 (0)15 2785574 A.O.Biffo@tudelft.nl Room: 2.01.170 C. Chen (Chaofan) +31 (0)15 2784745 C.Chen-9@tudelft.nl Room: 2.01.080 T. Gu (Tian) t.gu@tudelft.nl Room: 2.01.050 R.E. Hogenbirk (Rijk) r.e.hogenbirk@tudelft.nl M. van Hulzen (Martijn) m.vanhulzen@tudelft.nl Room: 2.01.070 R. van der Jagt (Remco) +31 (0)15 2784745 r.vanderjagt@tudelft.nl Room: 2.01.080 L.K. Kiriinya (Lindah) L.K.Kiriinya@tudelft.nl A.D. de Kogel (Albert) a.d.dekogel@tudelft.nl X. Kouoi (Xavier) +31 (0)15 2785574 X.Kouoi@tudelft.nl Room: 2.01.170 A.K. Kodyingal (Anish) a.k.kodyingal@tudelft.nl M.C. Kwakernaak (Mark) M.C.Kwakernaak@tudelft.nl V.R. Landgraf (Victor) +31 (0)15 2786964 V.R.Landgraf@tudelft.nl Room: 2.01.070 A.K. Lavrinenko (Anastasiia) +31 (0)15 2785574 A.K.Lavrinenko@tudelft.nl Room: 2.01.170 W.J. Legerstee (Walter) +31 (0)15 2783673 w.j.legerstee@tudelft.nl Room: 2.01.230 L. Maran (Luca) +31 (0)15 2783021 l.maran@tudelft.nl Room: 2.01.190 I. van Ogtrop (Ilse) i.vanogtrop@tudelft.nl P. Ombrini (Pierfrancesco) +31 (0)15 2784745 P.Ombrini-1@tudelft.nl Room: 2.01.080 M. Tu (Meng-Fu) m.tu@tudelft.nl Room: 2.01.070 H. Wang (Hao) +31 (0)15 2784745 H.Wang-20@tudelft.nl Room: 2.01.080 Z. Yuan (Ziqing) Z.Yuan-2@tudelft.nl S. Zhang (Shengnan) +31 (0)15 2786864 S.Zhang-16@tudelft.nl Room: 2.01.070 W. Zhao (Wenxuan) +31 (0)15 27 85574 w.zhao-5@tudelft.nl Room: 2.01.170 MSc – BSc - graduate students A.L. Dersjant (Alinda) a.l.dersjant@student.tudelft.nl T. Mulder (Tim) t.mulder@student.tudelft.nl I.J. Bax (Ivo) i.j.bax@student.tudelft.nl N.J. Bergsma (Niels) n.j.bergsma@student.tudelft.nl L. Bikker (Luca) M. Bulale (Mohammed) m.bulale@student.tudelft.nl C. Chen (Shichang) s.chen-72@student.tudelft.nl E. van Citteren E.vanCitteren@student.tudelft.nl H. Hanisch (Henning) h.m.hanisch@student.tudelft.nl E. Kirtosun (Erkay) e.kirtosun@student.tudelft.nl J.S. Kreikamp (Jasper) j.s.kreikamp@student.tudelft.nl M.J.H. Kurstjens (Maarten) m.j.h.kurstjens@student.tudelft.nl A. Schipper (Agnes) a.f.schipper@student.tudelft.nl H. Segers (Hidde) h.a.v.segers@student.tudelft.nl A. Wei (Ankang) a.wei@student.tudelft.nl E. Voorrips (Ewout) e.d.voorrips@student.tudelft.nl Guests dr. P. Braga Groszewicz (Pedro) p.groszewicz@tudelft.nl Publications ( Google Scholar ) T. Famprikis (Theo) +31 (0)15 2784758 t.famprikis@tudelft.nl K.N.E.K. Touidjine (Kaouther) k.n.e.k.touidjine@tudelft.nl

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New LDE trainee in D&I office

Keehan Akbari has started since the beginning of September as a new LDE trainee in the Diversity and Inclusion office. What motivated him to work for the D&I office, what does he expect to achieve during this traineeship? Read the short interview below! What motivated you to pursue your LDE traineeship in Diversity and Inclusion office of the TU Delft? I completed both bachelor's and master's degrees in Cultural Anthropology and Development Sociology at Leiden University. Within these studies, my main area of interest was in themes of inclusion and diversity. After being hired as a trainee for the LDE traineeship, and discovering that one of the possible assignments belonged to the Diversity and Inclusion office, my choice was quickly made. I saw this as an excellent opportunity to put the theories I learned during my studies into practice. What specific skills or experiences do you bring to the D&I office that will help promote inclusivity on campus? I am someone who likes to connect rather than polarize, taking into account the importance of different perspectives and stakeholders. I believe that this is how one can achieve the most in fostering diversity and inclusion. You need to get multiple parties on board to get the best results. What are your main goals as you begin your role here, and how do you hope to make an impact? An important goal for me this year is to get students more involved in diversity and inclusion at the university. One way I will try to accomplish this is by contributing to the creation of D&I student teams. By establishing a D&I student team for faculties, it will be possible to deal with diversity- and inclusion-related issues that apply and relate to the specific department. How do you plan to engage with different (student) communities within the university? Since I am new to TU Delft, the first thing I need to do is expand my network here. Therefore, I am currently busy exploring the university and getting to know various stakeholders. Moreover, I intend to be in close contact with various student and study organizations to explore together how to strengthen cooperation on diversity and inclusion. Welcome to the team Keehan and we wish you lots of success with your traineeship!

Researchers from TU Delft and Cambridge University collaborate on innovative methods to combat Climate Change

For over a year and a half, researchers from TU Delft and the Cambridge University Centre for Climate Repair have worked together on groundbreaking techniques to increase the reflectivity of clouds in the fight against global warming. During a two-day meeting, the teams are discussing their progress. Researchers at Cambridge are focusing on the technical development of a system that can spray seawater, releasing tiny salt crystals into the atmosphere to brighten the clouds. The team from TU Delft, led by Prof. Dr. Ir. Herman Russchenberg, scientific director of the TU Delft Climate Action Program and professor of Atmospheric Remote Sensing, is studying the physical effects of this technique. Prof. Russchenberg emphasizes the importance of this research: "We have now taken the first steps towards developing emergency measures against climate change. If it proves necessary, we must be prepared to implement these techniques. Ideally, we wouldn't need to use them, but it's important to investigate how they work now." Prof. Dr. Ir. Stefan Aarninkhof, dean of the Faculty of Civil Engineering and Geosciences, expresses pride in the team as the first results of this unique collaboration are becoming visible. If the researchers in Delft and Cambridge can demonstrate the potential of the concept, the first small-scale experiments will responsibly begin within a year. This research has been made possible thanks to the long-term support from the Refreeze the Arctic Foundation, founded by family of TU Delft alumnus Marc Salzer Levi . Such generous contributions enable innovative and high-impact research that addresses urgent global challenges like climate change. Large donations like these enable the pursuit of innovative, high-impact research that may not otherwise be feasible, demonstrating how our collective effort and investment in science can lead to real, transformative solutions for global challenges like climate change. Climate-Action Programme

How system safety can make Machine Learning systems safer in the public sector

Machine Learning (ML), a form of AI where patterns are discovered in large amounts of data, can be very useful. It is increasingly used, for example, in chatbot Chat GPT, facial recognition, or speech software. However, there are also concerns about the use of ML systems in the public sector. How do you prevent the system from, for example, discriminating or making large-scale mistakes with negative effects on citizens? Scientists at TU Delft, including Jeroen Delfos, investigated how lessons from system safety can contribute to making ML systems safer in the public sector. “Policymakers are busy devising measures to counter the negative effects of ML. Our research shows that they can rely much more on existing concepts and theories that have already proven their value in other sectors,” says Jeroen Delfos. Jeroen Delfos Learning from other sectors In their research, the scientists used concepts from system safety and systems theory to describe the challenges of using ML systems in the public sector. Delfos: “Concepts and tools from the system safety literature are already widely used to support safety in sectors such as aviation, for example by analysing accidents with system safety methods. However, this is not yet common practice in the field of AI and ML. By applying a system-theoretical perspective, we view safety not only as a result of how the technology works, but as the result of a complex set of technical, social, and organisational factors.” The researchers interviewed professionals from the public sector to see which factors are recognized and which are still underexposed. Bias There is room for improvement to make ML systems in the public sector safer. For example, bias in data is still often seen as a technical problem, while the origin of that bias may lie far outside the technical system. Delfos: “Consider, for instance, the registration of crime. In neighbourhoods where the police patrol more frequently, logically, more crime is recorded, which leads to these areas being overrepresented in crime statistics. An ML system trained to discover patterns in these statistics will replicate or even reinforce this bias. However, the problem lies in the method of recording, not in the ML system itself.” Reducing risks According to the researchers, policymakers and civil servants involved in the development of ML systems would do well to incorporate system safety concepts. For example, it is advisable to identify in advance what kinds of accidents one wants to prevent when designing an ML system. Another lesson from system safety, for instance in aviation, is that systems tend to become more risky over time in practice, because safety becomes subordinate to efficiency as long as no accidents occur. “It is therefore important that safety remains a recurring topic in evaluations and that safety requirements are enforced,” says Delfos. Read the research paper .