Events
Scientific machine learning (SciML) has been taking the academic world by storm as an interesting blend of traditional scientific modeling with machine learning (ML) methodologies like deep learning. While traditional machine learning methodologies have difficulties with scientific issues like interpretability, and enforcing physical constraints, the blend of ML with numerical analysis and differential equations has evolved into a novel field of research which overcome these problems while adding the data-driven automatic learning features of modern machine learning. Many successes have already been demonstrated, with tools like physics-informed neural networks, universal differential equations, deep backward stochastic differential equation solvers for high dimensional partial differential equations, and neural surrogates showcasing how deep learning can greatly improve scientific modeling practice. Consequently, SciML holds promise for versatile application across a wide spectrum of scientific disciplines, ranging from the investigation of subatomic particles to the comprehension of macroscopic systems like economies and climates.
However, despite notable strides in enhancing the speed and accuracy of these methodologies, their utility in practical and specifically industrial settings remain constrained. Many domains within the scientific community still lack comprehensive validation and robustness testing of SciML approaches. This limitation is particularly pronounced when confronted with complex, real-world datasets emanating from interactions between machinery and environmental sensors as usually addressed in industry. Still if appropriately addressed, SciML with its promise to accelerate innovations and scientific discoveries by orders of magnitudes, offers unique opportunities to address the insatiable desire for faster and more accurate predictions in many fields.
This presentation is dedicated to exploring recent advancements in the implementation of SciML techniques. We will discuss how methodologies can be refined to ensure their practical viability and scalability, particularly in industrial sectors where digital and physical components converge.
Contatto:
paola.antonietti@polimi.it
Wil Schilders studied Mathematics, with Physics and Astronomy, at the Radboud University in Nijmegen, The Netherlands, from 1974-1978, and obtained his PhD in numerical analysis from Trinity College Dublin in 1980. From 1980-2006 he worked at Philips Research, performing research on mathematical methods and software for semiconductor device simulation and electronic circuit simulation, and from 2006-2010 at NXP Semiconductors. Since 1999, he was also a part-time professor at TU Eindhoven on scientific computing for industry. In 2010, he moved to TU Eindhoven, and also became the director of the Dutch Platform for Mathematics. He has been active within the European Consortium for Mathematics in Industry (ECMI), being president in 2010-2011 and chairing the Research and Innovation Committee for many years. From 2015-20, he was president of EU-MATHS-IN, the European Service Network of Mathematics for Industry and Innovation (www.eu-maths-in.eu). Since October 1, 2023, he is the president of the International Council for Industrial and Applied Mathematics (ICIAM). In 2020, he was the 4th Mittelsten-Scheid guest professor at Bergische Universitaet Wuppertal, and since 2021 he is a Hans Fischer Senior Fellow at the Institute for Advanced Study at TU Munich. He is a fellow of the Society for Industrial and Applied Mathematics (SIAM) and was awarded the Dutch Stairway to Impact award end of 2022. In 2023, he organized the SIAM conference on Computational Science and Engineering in Amsterdam, with 2100+ participants. He supervised 25 PhD students, and led more than 10 European projects. His main expertise is in numerical linear algebra, model order reduction (he was chair of EU-MORNET) and recently he has become interested in scientific machine learning, a combination of numerical analysis/scientific computing and machine learning (his motto: ‘’Real intelligence is needed to make artificial intelligence work’’). He has a large network, also with industry, and is very interested in sustainability and the role of mathematics herein.
Structurally, brain tissue is characterized by thin cell membranes and slender vessels, defining submanifolds of codimension one and two respectively. Functionally, your brain fundamentally relies on the transport of ions and nutrients and movement of water in and between these spaces. These physiological processes are clearly crucial for brain function and health, but the precise mechanisms and their association with neurodegenerative diseases such as Alzheimer's and Parkinson's disease and neurological events such as seizures remain only partially understood. Notably, mathematical and computational modelling are beginning to play an important role in gaining new insight. In this talk, I will discuss key mathematical, numerical and computational challenges associated with modelling brain mechanics and transport across scales with an emphasis on coupled systems of partial differential equations with dimensional gaps.
Contatti:
paola.antonietti@polimi.it
Marie E. Rognes is Chief Research Scientist in Scientific Computing and Numerical Analysis at Simula Research Laboratory, Oslo, Norway. Her research focuses on computational mathematics and its applications in the life sciences in general and neuroscience in particular. She received her Ph.D from the University of Oslo in 2009 after an extended research stay at the University of Minnesota Twin Cities, Minneapolis, US. She has been at Simula Research Laboratory since 2009, and led its Department for Biomedical Computing from 2012 to 2016. She held a Professor II position (20%) at the Department of Mathematics, University of Bergen, Norway (2020-2022), and was a Visiting Fulbright Scholar at the Institute for Engineering in Medicine, University of California San Diego, CA, US (2022-2023).
Rognes is a member of the Norwegian Academy for Technological Sciences (2022-) and was a Founding Member of the Young Academy of Norway in 2016. She won the 2015 Wilkinson Prize for Numerical Software, the 2018 Royal Norwegian Society of Sciences and Letters Prize for Young Researchers within the Natural Sciences, an ERC Starting Grant in Mathematics in 2017, and is the principal recipient of several ground-breaking research grants from the Research Council of Norway. She is (or has been) a member of the Research Council of Norway's Portfolio Board for ground-breaking research (2024-), the European Mathematical Society's Committee for Applications and Interdisciplinary Relations (2023-), the Interpore Council (2023-), and the FEniCS Steering Council (2016-2024), in addition to six Editorial Boards spanning pure and applied mathematics, scientific computing and mathematical software. Rognes has supervised more than 8 postdoctoral fellows, 16 PhD or DPhil students, and 13 MSc students in the period 2012-2024.
Structurally, brain tissue is characterized by thin cell membranes and slender vessels, defining submanifolds of codimension one and two respectively. Functionally, your brain fundamentally relies on the transport of ions and nutrients and movement of water in and between these spaces. These physiological processes are clearly crucial for brain function and health, but the precise mechanisms and their association with neurodegenerative diseases such as Alzheimer's and Parkinson's disease and neurological events such as seizures remain only partially understood. Notably, mathematical and computational modelling are beginning to play an important role in gaining new insight. In this talk, I will discuss key mathematical, numerical and computational challenges associated with modelling brain mechanics and transport across scales with an emphasis on coupled systems of partial differential equations with dimensional gaps.
Contatti:
paola.antonietti@polimi.it
Marie E. Rognes is Chief Research Scientist in Scientific Computing and Numerical Analysis at Simula Research Laboratory, Oslo, Norway. Her research focuses on computational mathematics and its applications in the life sciences in general and neuroscience in particular. She received her Ph.D from the University of Oslo in 2009 after an extended research stay at the University of Minnesota Twin Cities, Minneapolis, US. She has been at Simula Research Laboratory since 2009, and led its Department for Biomedical Computing from 2012 to 2016. She held a Professor II position (20%) at the Department of Mathematics, University of Bergen, Norway (2020-2022), and was a Visiting Fulbright Scholar at the Institute for Engineering in Medicine, University of California San Diego, CA, US (2022-2023).
Rognes is a member of the Norwegian Academy for Technological Sciences (2022-) and was a Founding Member of the Young Academy of Norway in 2016. She won the 2015 Wilkinson Prize for Numerical Software, the 2018 Royal Norwegian Society of Sciences and Letters Prize for Young Researchers within the Natural Sciences, an ERC Starting Grant in Mathematics in 2017, and is the principal recipient of several ground-breaking research grants from the Research Council of Norway. She is (or has been) a member of the Research Council of Norway's Portfolio Board for ground-breaking research (2024-), the European Mathematical Society's Committee for Applications and Interdisciplinary Relations (2023-), the Interpore Council (2023-), and the FEniCS Steering Council (2016-2024), in addition to six Editorial Boards spanning pure and applied mathematics, scientific computing and mathematical software. Rognes has supervised more than 8 postdoctoral fellows, 16 PhD or DPhil students, and 13 MSc students in the period 2012-2024.
The talk overviews recent research by the authors on the development of second-order consistent and stable lattice Boltzmann formulations to solve elastostatics and elastodynamics problems. The first proposed scheme [1] solves the quasi-static equations of linear elasticity in two dimensions using a collision operator with multiple relaxation times. In contrast to previous works, our formulation solves for a single distribution function with a standard velocity set and avoids any recourse to finite difference approximations. As a result, all computational benefits of the lattice Boltzmann method can be used to full capacity. The second proposed scheme [2] solves the equations of linear elastodynamics in two dimensions (the extension to three dimensions is currently also available but still unpublished). The construction of the numerical scheme uses an equivalent first-order hyperbolic system of equations as an intermediate step, for which a vectorial lattice Boltzmann formulation is introduced. The only difference to conventional lattice Boltzmann formulations is the usage of vector-valued populations, so that once again all computational benefits of the algorithm are preserved. Both schemes are systematically derived using the asymptotic expansion technique. Stability is assessed for elastostatics with von Neumann analysis, whereas in elastodynamics we exploit the notion of pre-stability structures to prove stability for an arbitrary combination of material parameters under a CFL-like condition. Boundary formulation for various cases are proposed [3]. All theoretical derivations are numerically verified by convergence studies using manufactured solutions and long-term stability tests.
[1] O. Boolakee, M. Geier, L. De Lorenzis (2023), A new Lattice Boltzmann scheme for linear elastic solids: periodic problems. Computer Methods in Applied Mechanics and Engineering, 404: 115756.
[2] O. Boolakee, M. Geier, L. De Lorenzis (2025). Lattice Boltzmann for linear elastodynamics: periodic problems and Dirichlet boundary conditions. Computer Methods in Applied Mechanics and Engineering, 433: 117469.
[3] O. Boolakee, M. Geier, L. De Lorenzis (2023), Dirichlet and Neumann boundary conditions for a lattice Boltzmann scheme for linear elastic solids on arbitrary domains. Computer Methods in Applied Mechanics and Engineering, 415: 116225.
Contatti:
davide.riccobelli@polimi.it
Laura De Lorenzis received her Engineering degree and her PhD from the University of her hometown Lecce, in southern Italy, where she first stayed as Assistant and later as Associate Professor of Solid and structural mechanics. In 2013 she moved to the TU Braunschweig, Germany, as Professor and Director of the Institute of Applied Mechanics. There she was founding member and first Chair (2017-2020) of the Center for Mechanics, Uncertainty and Simulation in Engineering. Since 2020 she is Professor of Computational Mechanics at ETH Zürich, in the Department of Mechanical and Process Engineering. She was visiting scholar in several renowned institutions, including Chalmers University of Technology, the Hong Kong Polytechnic University, the Massachusetts Institute of Technology (as holder of a Fulbright Fellowship in 2006), the Leibniz University of Hannover (with an Alexander von Humboldt Fellowship in 2010-2011), the University of Texas at Austin and the University of Cape Town. She is the recipient of several prizes, including the RILEM L’Hermite Medal 2011, the AIMETA Junior Prize 2011, the IIFC Young Investigator Award 2012, the Euromech Solid Mechanics Fellowship 2022, the IACM Fellowship 2024, two best paper awards and two student teaching prizes. In 2011 she was awarded a European Research Council Starting Researcher Grant. She has authored or co-authored more than 150 papers on international journals on different topics of computational and applied mechanics. Since 2023 she is Editor of Computer Methods in Applied Mechanics and Engineering.
The talk overviews recent research by the authors on the development of second-order consistent and stable lattice Boltzmann formulations to solve elastostatics and elastodynamics problems. The first proposed scheme [1] solves the quasi-static equations of linear elasticity in two dimensions using a collision operator with multiple relaxation times. In contrast to previous works, our formulation solves for a single distribution function with a standard velocity set and avoids any recourse to finite difference approximations. As a result, all computational benefits of the lattice Boltzmann method can be used to full capacity. The second proposed scheme [2] solves the equations of linear elastodynamics in two dimensions (the extension to three dimensions is currently also available but still unpublished). The construction of the numerical scheme uses an equivalent first-order hyperbolic system of equations as an intermediate step, for which a vectorial lattice Boltzmann formulation is introduced. The only difference to conventional lattice Boltzmann formulations is the usage of vector-valued populations, so that once again all computational benefits of the algorithm are preserved. Both schemes are systematically derived using the asymptotic expansion technique. Stability is assessed for elastostatics with von Neumann analysis, whereas in elastodynamics we exploit the notion of pre-stability structures to prove stability for an arbitrary combination of material parameters under a CFL-like condition. Boundary formulation for various cases are proposed [3]. All theoretical derivations are numerically verified by convergence studies using manufactured solutions and long-term stability tests.
[1] O. Boolakee, M. Geier, L. De Lorenzis (2023), A new Lattice Boltzmann scheme for linear elastic solids: periodic problems. Computer Methods in Applied Mechanics and Engineering, 404: 115756.
[2] O. Boolakee, M. Geier, L. De Lorenzis (2025). Lattice Boltzmann for linear elastodynamics: periodic problems and Dirichlet boundary conditions. Computer Methods in Applied Mechanics and Engineering, 433: 117469.
[3] O. Boolakee, M. Geier, L. De Lorenzis (2023), Dirichlet and Neumann boundary conditions for a lattice Boltzmann scheme for linear elastic solids on arbitrary domains. Computer Methods in Applied Mechanics and Engineering, 415: 116225.
Contatti:
davide.riccobelli@polimi.it
Laura De Lorenzis received her Engineering degree and her PhD from the University of her hometown Lecce, in southern Italy, where she first stayed as Assistant and later as Associate Professor of Solid and structural mechanics. In 2013 she moved to the TU Braunschweig, Germany, as Professor and Director of the Institute of Applied Mechanics. There she was founding member and first Chair (2017-2020) of the Center for Mechanics, Uncertainty and Simulation in Engineering. Since 2020 she is Professor of Computational Mechanics at ETH Zürich, in the Department of Mechanical and Process Engineering. She was visiting scholar in several renowned institutions, including Chalmers University of Technology, the Hong Kong Polytechnic University, the Massachusetts Institute of Technology (as holder of a Fulbright Fellowship in 2006), the Leibniz University of Hannover (with an Alexander von Humboldt Fellowship in 2010-2011), the University of Texas at Austin and the University of Cape Town. She is the recipient of several prizes, including the RILEM L’Hermite Medal 2011, the AIMETA Junior Prize 2011, the IIFC Young Investigator Award 2012, the Euromech Solid Mechanics Fellowship 2022, the IACM Fellowship 2024, two best paper awards and two student teaching prizes. In 2011 she was awarded a European Research Council Starting Researcher Grant. She has authored or co-authored more than 150 papers on international journals on different topics of computational and applied mechanics. Since 2023 she is Editor of Computer Methods in Applied Mechanics and Engineering.
The quaternionic (or Clifford algebra) version of the Cauchy integral formula motivates the so called bounded S-functional calculus, i.e., we formally replace the variable which is not integrated in the Cauchy integral formula by a bounded operator T.
For bounded operators, this integral makes sense, since the spectrum of T is bounded and the integration path is compact.
For unbounded, closed operators T, there are different generalizations of the functional calculus. In particular, for the important class of sectorial operators, this talk will introduce the H^\infty-functional calculus in a 2- step procedure. First, functions f with a certain decay at infinity are considered, enough decay such that the integral still makes sense. In a second step, using a regularization procedure, f(T) is defined also for polynomially growing functions.
Laura De Lorenzis received her Engineering degree and her PhD from the University of her hometown Lecce, in southern Italy, where she first stayed as Assistant and later as Associate Professor of Solid and structural mechanics. In 2013 she moved to the TU Braunschweig, Germany, as Professor and Director of the Institute of Applied Mechanics. There she was founding member and first Chair (2017-2020) of the Center for Mechanics, Uncertainty and Simulation in Engineering. Since 2020 she is Professor of Computational Mechanics at ETH Zürich, in the Department of Mechanical and Process Engineering. She was visiting scholar in several renowned institutions, including Chalmers University of Technology, the Hong Kong Polytechnic University, the Massachusetts Institute of Technology (as holder of a Fulbright Fellowship in 2006), the Leibniz University of Hannover (with an Alexander von Humboldt Fellowship in 2010-2011), the University of Texas at Austin and the University of Cape Town. She is the recipient of several prizes, including the RILEM L’Hermite Medal 2011, the AIMETA Junior Prize 2011, the IIFC Young Investigator Award 2012, the Euromech Solid Mechanics Fellowship 2022, the IACM Fellowship 2024, two best paper awards and two student teaching prizes. In 2011 she was awarded a European Research Council Starting Researcher Grant. She has authored or co-authored more than 150 papers on international journals on different topics of computational and applied mechanics. Since 2023 she is Editor of Computer Methods in Applied Mechanics and Engineering.
Motivated by the various Dirac equations in geometry and physics, we consider the nodal set of solutions to a class of Dirac equations. In contrast to scalar function case, we show that the nodal sets in general has codimension at least two, which strengthen the known results in the smooth setting and confirms a conjecture in spin geometry.
Moreover, using a spinorial version of the frequency function, we show that the nodal set can be stratified nicely.
This is based on a joint work with A. Malchiodi and W. Borrelli.
Laura De Lorenzis received her Engineering degree and her PhD from the University of her hometown Lecce, in southern Italy, where she first stayed as Assistant and later as Associate Professor of Solid and structural mechanics. In 2013 she moved to the TU Braunschweig, Germany, as Professor and Director of the Institute of Applied Mechanics. There she was founding member and first Chair (2017-2020) of the Center for Mechanics, Uncertainty and Simulation in Engineering. Since 2020 she is Professor of Computational Mechanics at ETH Zürich, in the Department of Mechanical and Process Engineering. She was visiting scholar in several renowned institutions, including Chalmers University of Technology, the Hong Kong Polytechnic University, the Massachusetts Institute of Technology (as holder of a Fulbright Fellowship in 2006), the Leibniz University of Hannover (with an Alexander von Humboldt Fellowship in 2010-2011), the University of Texas at Austin and the University of Cape Town. She is the recipient of several prizes, including the RILEM L’Hermite Medal 2011, the AIMETA Junior Prize 2011, the IIFC Young Investigator Award 2012, the Euromech Solid Mechanics Fellowship 2022, the IACM Fellowship 2024, two best paper awards and two student teaching prizes. In 2011 she was awarded a European Research Council Starting Researcher Grant. She has authored or co-authored more than 150 papers on international journals on different topics of computational and applied mechanics. Since 2023 she is Editor of Computer Methods in Applied Mechanics and Engineering.
Per un'equazione deterministica di Schrödinger si mostra l'esistenza di soluzioni statistiche stazionarie ottenute come opportuno limite della soluzione della corrispondente EDP perturbata con una forzante stocastica e una dissipazione lineare. Inoltre si analizzano le proprietà di questi processi stazionari.
Laura De Lorenzis received her Engineering degree and her PhD from the University of her hometown Lecce, in southern Italy, where she first stayed as Assistant and later as Associate Professor of Solid and structural mechanics. In 2013 she moved to the TU Braunschweig, Germany, as Professor and Director of the Institute of Applied Mechanics. There she was founding member and first Chair (2017-2020) of the Center for Mechanics, Uncertainty and Simulation in Engineering. Since 2020 she is Professor of Computational Mechanics at ETH Zürich, in the Department of Mechanical and Process Engineering. She was visiting scholar in several renowned institutions, including Chalmers University of Technology, the Hong Kong Polytechnic University, the Massachusetts Institute of Technology (as holder of a Fulbright Fellowship in 2006), the Leibniz University of Hannover (with an Alexander von Humboldt Fellowship in 2010-2011), the University of Texas at Austin and the University of Cape Town. She is the recipient of several prizes, including the RILEM L’Hermite Medal 2011, the AIMETA Junior Prize 2011, the IIFC Young Investigator Award 2012, the Euromech Solid Mechanics Fellowship 2022, the IACM Fellowship 2024, two best paper awards and two student teaching prizes. In 2011 she was awarded a European Research Council Starting Researcher Grant. She has authored or co-authored more than 150 papers on international journals on different topics of computational and applied mechanics. Since 2023 she is Editor of Computer Methods in Applied Mechanics and Engineering.
Calcoleremo l'integrale definito della funzione potenza x^a, per via diretta, facendo uso solo della definizione di integrale definito, senza sfruttare il teorema fondamentale del calcolo. Nel caso a=-1, attraverso la funzione integrale di 1/x definiremo la funzione logaritmo naturale e ne dedurremo alcune proprietà.
Laura De Lorenzis received her Engineering degree and her PhD from the University of her hometown Lecce, in southern Italy, where she first stayed as Assistant and later as Associate Professor of Solid and structural mechanics. In 2013 she moved to the TU Braunschweig, Germany, as Professor and Director of the Institute of Applied Mechanics. There she was founding member and first Chair (2017-2020) of the Center for Mechanics, Uncertainty and Simulation in Engineering. Since 2020 she is Professor of Computational Mechanics at ETH Zürich, in the Department of Mechanical and Process Engineering. She was visiting scholar in several renowned institutions, including Chalmers University of Technology, the Hong Kong Polytechnic University, the Massachusetts Institute of Technology (as holder of a Fulbright Fellowship in 2006), the Leibniz University of Hannover (with an Alexander von Humboldt Fellowship in 2010-2011), the University of Texas at Austin and the University of Cape Town. She is the recipient of several prizes, including the RILEM L’Hermite Medal 2011, the AIMETA Junior Prize 2011, the IIFC Young Investigator Award 2012, the Euromech Solid Mechanics Fellowship 2022, the IACM Fellowship 2024, two best paper awards and two student teaching prizes. In 2011 she was awarded a European Research Council Starting Researcher Grant. She has authored or co-authored more than 150 papers on international journals on different topics of computational and applied mechanics. Since 2023 she is Editor of Computer Methods in Applied Mechanics and Engineering.
Neural Bayes estimators are neural networks that approximate Bayes estimators. They are thus likelihood-free, extremely fast to evaluate, and amenable to rapid uncertainty quantification, while also (approximately) inheriting the appealing large-sample properties of Bayes estimators. Neural Bayes estimators are therefore ideal to use with spatial extremes models observed in high dimensions, where estimation is often a computational bottleneck. In this seminar, I will summarize our research progress in that area and explain how, for any spatial model that can be simulated from, a single neural Bayes estimator can be trained to make fast inference with new data that involve varying sample sizes, varying spatial configurations of observed locations, and varying censoring levels used in peaks-over-threshold modeling. This methodology will be illustrated by application to sea surface temperature extremes over the Red Sea, and air pollution extremes over the whole Arabic peninsula. Joint work with Jordan Richards, Matthew Sainsbury-Dale, and Andrew Zammit-Mangion. This initiative is part of the “Ph.D. Lectures” activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk. Contact: alessandra.menafoglio@polimi.it
Laura De Lorenzis received her Engineering degree and her PhD from the University of her hometown Lecce, in southern Italy, where she first stayed as Assistant and later as Associate Professor of Solid and structural mechanics. In 2013 she moved to the TU Braunschweig, Germany, as Professor and Director of the Institute of Applied Mechanics. There she was founding member and first Chair (2017-2020) of the Center for Mechanics, Uncertainty and Simulation in Engineering. Since 2020 she is Professor of Computational Mechanics at ETH Zürich, in the Department of Mechanical and Process Engineering. She was visiting scholar in several renowned institutions, including Chalmers University of Technology, the Hong Kong Polytechnic University, the Massachusetts Institute of Technology (as holder of a Fulbright Fellowship in 2006), the Leibniz University of Hannover (with an Alexander von Humboldt Fellowship in 2010-2011), the University of Texas at Austin and the University of Cape Town. She is the recipient of several prizes, including the RILEM L’Hermite Medal 2011, the AIMETA Junior Prize 2011, the IIFC Young Investigator Award 2012, the Euromech Solid Mechanics Fellowship 2022, the IACM Fellowship 2024, two best paper awards and two student teaching prizes. In 2011 she was awarded a European Research Council Starting Researcher Grant. She has authored or co-authored more than 150 papers on international journals on different topics of computational and applied mechanics. Since 2023 she is Editor of Computer Methods in Applied Mechanics and Engineering.
Mathematical Seminars
Politecnico di Milano
- Analisi
- Cultura Matematica
- Seminari FDS
- Geometry and Algebra
- Probabilità e Statistica Matematica
- Probabilità Quantistica