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"If there were no difference between essence and appearance, there would be no need for science"
My research lies in the areas of Numerical Analysis, Scientific Machine Learning and Scientific Computing for complex and multiscale dynamical systems. The scientific keystones of the research integrate Numerical Analysis, Machine Learning and Manifold Learning, Operators, Data-Mining, Complex Systems, Nonlinear Systems, Bifurcation theory, and Control theory. All in all, I am trying to tackle the "curse of dimensionality" by developing explainable SciML methods with the aid of niche numerical analysis to solve both the forward and importantly the inverse problem in complex and multiscale dynamical systems.
My research lies in the areas of Numerical Analysis, Scientific Machine Learning and Scientific Computing for complex and multiscale dynamical systems. The scientific keystones of the research integrate Numerical Analysis, Machine Learning and Manifold Learning, Operators, Data-Mining, Complex Systems, Nonlinear Systems, Bifurcation theory, and Control theory. All in all, I am trying to tackle the "curse of dimensionality" by developing explainable SciML methods with the aid of niche numerical analysis to solve both the forward and importantly the inverse problem in complex and multiscale dynamical systems.
firstname.lastname at unina dot the alpha-2 country code
Recent Publications
Recent Publications
Featured Article
News!
I am glad to share that the recent Nature Machine Intelligence Editorial, “Solutions, challenges and rising tensions in AI and mathematics,” explicitly highlights my accompanying invited News & Views article, “Neural operators for free-boundary problems.”
🧠 The editorial discusses how artificial intelligence is increasingly interacting with mathematics, creating new opportunities while also raising important scientific and conceptual challenges. In referring to my contribution, it emphasizes the importance of incorporating new mathematical theories to deal with challening real-world problems with sharp, potentially irreversible (catastrophic) transitions, such as glacial ice melting under climate change and tumour growth during cancer therapy.
🧮 In the invited News & Views, I discuss how the mathematical principle of topological conjugacy can extend neural operators to free-boundary problems, in which both the solution and the geometry of the domain evolve over time.
🔗 This perspective also connects naturally with our recently published research article in Nature Machine Intelligence, “Enabling local neural operators to perform equation-free system-level analysis,” presented in an earlier post. Developed in collaboration with Gianluca Fabiani, Hannes Vandecasteele, Somdatta Goswami and Ioannis Kevrekidis from The Johns Hopkins University , the work combines local neural operators with equation-free methods, Newton–Krylov solvers, Arnoldi algorithms and numerical continuation to perform stability and bifurcation analysis of complex and multiscale systems directly from sparse spatiotemporal data.
🌐 Together, these contributions reflect an increasingly important research direction: combining artificial intelligence, mathematical analysis and advanced numerical methods to develop reliable scientific machine-learning tools to deal with real-world complex systems and their emergent dynamics.
📄 Editorial:
📘 Invited News & Views:
🔁 My previous post on the research article:https://lnkd.in/dyFWn5jJ
International Conference on Applied Mathematics 2026/ Celebrating the William Benter Prize forProf. George Karniadakis , Bie Ju Centre for Mathematical Sciences, City U Hong Kong, 9 - 12 June 2026, Invited Speaker: Physics-informed, physics-free, and numerical analysis-informed machine learning for Complex systems.
Days of Applied NOnlinearity and Complexity (DANOC) , 23 - 25 January 2026, Plenary/Keynote Speaker: Explainable Numerical Analysis-Informed Machine Learning for Complex Systems.
International Conference "Scientific Machine Learning, emerging topics", Trieste, SISSA, Italy, 18-21 June 2024, Plenary/Keynote Speaker: Solving the inverse problem in complex systems via machine learning: challenges and perspectives
21st Summer Meeting in Risk Finance and Stochastics, 9 - 13 September 2024, Athens University of Economic and Business, Hybrid, Plenary/Keynote Speaker: Mind the gap between deep neural networks and numerical analysis tasks.
Machine Learning + X Seminar Series, Division of Applied Mathematics, Brown University, USA, 21 April 2023, Invited Seminar Lecture. From Physics-Informed to Physics-Free Control of Complex Systems via Machine Learning. https://www.brown.edu/research/projects/crunch/machine-learning-x-seminars/machine-learning-x-seminars-2023. You can find the video of the presentation here: https://youtu.be/W-gda3cW028
Machine Learning + X Seminar Series, Division of Applied Mathematics, Brown University, USA, 21 April 2023, Invited Seminar Lecture. From Physics-Informed to Physics-Free Control of Complex Systems via Machine Learning. https://www.brown.edu/research/projects/crunch/machine-learning-x-seminars/machine-learning-x-seminars-2023. You can find the video of the presentation here: https://youtu.be/W-gda3cW028
30th Summer School and Conference on Dynamic Systems & Complexity , Calandra University Camping, Halkidiki, 28/8/2024 – 6/9/2024. Plenary /Keynote Speaker: An introduction to scientific machine learning for the solution of the forward and inverse problems in dynamical systems. Challenges and Perspectives.
14th Conference, Dynamical Systems in Biology and Natural Sciences, February 3-8, 2023, Bilbao, Spain, Plenary'Keynote Speaker. Numerical Solution of the forward and inverse problems in complex dynamical modelling and analysis with manifold learning and physics-informed random projection neural networks https://sites.google.com/bcamath.org/dsabns2023/home
14th Conference, Dynamical Systems in Biology and Natural Sciences, February 3-8, 2023, Bilbao, Spain, Plenary'Keynote Speaker. Numerical Solution of the forward and inverse problems in complex dynamical modelling and analysis with manifold learning and physics-informed random projection neural networks https://sites.google.com/bcamath.org/dsabns2023/home
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