This Week at ICERM
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March 17, 2024
There are no events currently scheduled for March 17th.
March 18, 2024
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3:30 - 4:00 pm EDTCoffee Break11th Floor Collaborative Space
March 19, 2024
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11:00 am - 12:00 pm EDTWaveHoltz: Parallel and Scalable Solution of the Helmholtz Equation via Wave Equation Iteration11th Floor Lecture Hall
- Daniel Appelö, Virginia Tech
Abstract
We introduce the WaveHoltz iteration, for solving the Helmholtz equation. The method is inspired by recent work on exact controllability (EC) methods and as in EC methods we make use of time domain methods for wave equations to design frequency domain Helmholtz solvers, but unlike EC methods we do not require adjoint solves. We show that the WaveHoltz iteration is symmetric and positive definite (compared to the indefinite Helmholtz equation). We present numerical examples, using various discretization techniques, that show that our method can be used to solve problems with rather high wave numbers.
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12:00 - 12:30 pm EDTHybridizable discontinuous Galerkin methodPost Doc/Graduate Student Seminar - 11th Floor Conference Room
- Yukun Yue, University of Wisconsin, Madison
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12:30 - 1:00 pm EDTPDE constrained optimizationPost Doc/Graduate Student Seminar - 11th Floor Conference Room
- Sijing Liu, Brown University
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3:30 - 4:00 pm EDTCoffee Break11th Floor Collaborative Space
March 20, 2024
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11:00 am - 12:00 pm EDTBabuska's paradox in linear and nonlinear bending theories11th Floor Lecture Hall
- Soeren Bartels, University of Freiburg
Abstract
The plate bending or Babuska paradox refers to the failure of convergence when a linear bending problem with simple support boundary conditions is approximated using polygonal domain approximations. We provide an explanation based on a variational viewpoint and identify sufficient conditions that avoid the paradox and which show that boundary conditions have to be suitably modified. We show that the paradox also matters in nonlinear thin-sheet folding problems and devise approximations that correctly converge to the original problem.
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3:30 - 4:00 pm EDTCoffee Break11th Floor Collaborative Space
March 21, 2024
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3:30 - 4:00 pm EDTCoffee Break11th Floor Collaborative Space
March 22, 2024
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3:30 - 4:00 pm EDTCoffee Break11th Floor Collaborative Space
March 23, 2024
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8:50 - 9:00 am EDTWelcome11th Floor Lecture Hall
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9:00 - 9:30 am EDTData-driven modelling to solve intractable physics11th Floor Lecture Hall
- Speaker
- Richard Ahfeld, Monolith
- Session Chair
- Marta D'Elia, Pasteur Labs. and Stanford University
Abstract
All engineering companies want to build high-quality products as efficiently and quickly as possible. Physics-based simulation or CAE can provide answers virtually and faster without building prototypes or performing tests. However, in a recent survey among 163 engineering leaders conducted by the market research institute Forrester*, 55% of leaders said that they found CAE too inaccurate. Despite years of continuous progress on CAE methods, there are still many problems for which solving PDEs does not provide accurate insights – either because the underlying physics is too complex, or the boundary conditions are insufficiently known. To give an example, calibrating a P2D model for battery simulation requires so much data of a real battery cell prototype, that the battery must already have been manufactured and have undergone a large number of tests before the model becomes useful. In a case like this, where the physics is intractable, data-driven simulation can be a faster and easier way to model and optimise system performs. Intractable physics problems are everywhere in engineering, from materials science to dynamic system behaviour. This talk will look at various industrial case studies in which data-driven modelling was used to accelerate product development, including the Porsche Jota race team who used data-driven models for tire degradation and won Le Mans, Honeywell who found that data-driven methods can beat CFD in ultra-sound flow measurement, Kautex Textron who developed a more accurate method to model fuel sloshing noise, as well as BMW group who managed to predict the result of crash tests without CAE. The talk will end by focusing on battery simulation. In the author’s opinion, this is the most impactful area of engineering where machine learning can help model intractable physics, as the electrochemical relationships of batteries are notoriously hard to model and require a huge of amount of time-consuming testing. *Commissioned by Monolith
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9:40 - 10:10 am EDTNVIDIA Modulus: An Open-Source Framework for Scientific Machine Learning11th Floor Lecture Hall
- Speaker
- Mohammad Nabian, Nvidia
- Session Chair
- Marta D'Elia, Pasteur Labs. and Stanford University
Abstract
High-fidelity simulations, crucial in science and engineering, are traditionally time-consuming and computationally demanding, hindering rapid iteration in various applications like design analysis and optimization. NVIDIA Modulus, a cutting-edge scientific machine learning platform, revolutionizes these processes by creating surrogate models that significantly outpace conventional methods in speed, maintaining high simulation accuracy. NVIDIA Modulus's surrogate models cater to diverse applications, such as weather prediction, power plant modeling, cardiovascular simulation, additive manufacturing, and aerodynamic evaluation. Modulus is accessible as open-source software under the Apache 2.0 license, fostering the expansion of the scientific machine learning community.
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10:20 - 10:50 am EDTCoffee Break11th Floor Collaborative Space
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10:50 - 11:20 am EDTMachine Learning and Reduced Order Modeling for Large-Scale Industrial Digital Twins11th Floor Lecture Hall
- Speaker
- David Knezevic, Akselos
- Session Chair
- Marta D'Elia, Pasteur Labs. and Stanford University
Abstract
Akselos provides Digital Twins of industrial equipment in a range of industries, such energy, renewables, mining, and aerospace. The Akselos platform is based on RB-FEA, which is a unique combination of the Reduced Basis method for fast reduced order modeling of parametrized PDEs, with a domain decomposition framework that enables large-scale component-based analysis. RB-FEA shares many similarities to supervised learning approaches, in which "full order" solutions are used as the "supervisor" during RB-FEA training. In this presentation we will discuss the similarities and differences between RB-FEA and other ML methods, and demonstrate applications of the methodology to industrial Digital Twins.
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11:30 am - 12:00 pm EDTA local, low-dimensional Machine Learning based PDE Solver for modeling engineering applications11th Floor Lecture Hall
- Speaker
- Rishikesh Ranade, ANSYS
- Session Chair
- Marta D'Elia, Pasteur Labs. and Stanford University
Abstract
In this talk, I will introduce a semi-supervised Machine Learning (ML) approach to model PDEs across a variety of engineering applications. The local, low-dimensional ML-Solver solves PDEs on multi-resolution meshes which are significantly coarser than the computational meshes used in typical engineering simulations. A coarse ML-Solver element, known as a subdomain, is representative of hundreds or even thousands of computational elements. The PDE solutions as well as other PDE conditions such as geometry, source terms and BCs are represented by n-dimensional latent vectors on each subdomain. The transformations between latent vectors and solution or condition fields on computational elements within a subdomain are learnt using field neural networks. Additionally, spatial, and temporal flux relationships between neighboring subdomains are learnt in the latent space using flux conservation neural networks and time integration neural networks. All the NNs are trained using data generated from engineering simulations. This talk will delve further into the nuts and bolts of the ML-Solver and demonstrate it across a variety of engineering use cases from fluids, thermal and mechanical applications. Finally, this talk will also demonstrate a use case of the ML-Solver that shows the potential of development towards a foundation model which can be used across a wide range of applications with consistent physics.
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12:10 - 2:00 pm EDTLunch/Free Time
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2:00 - 2:30 pm EDTQuasi Real-Time Simulations with Neural Networks for Industrial Applications11th Floor Lecture Hall
- Speaker
- Yu-Chin Chan, Siemens Technology
- Session Chair
- George Karniadakis, Brown University
Abstract
From reduced order models to PINNs and neural operators, the exponential growth of neural network techniques has shifted industry toward a new paradigm: scientific machine learning (SciML). However, industrial use cases are becoming increasingly complex while demanding faster, near real-time turnaround, necessitating the adaption of SciML to drastically more difficult problems. At Siemens Technology, we are researching the latest machine learning advances to develop solutions for our businesses and products. In this talk, we present an overview of interesting applications of SciML for Siemens, and our recent work on accelerating digital twins for a variety of use cases, including inverse heat exchanger control, quasi real-time prediction of airbag deployment, and neural design optimization in large design spaces. Through these examples, we also share some challenges in applying SciML to industrial applications.
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2:40 - 3:10 pm EDTEnforcing Structure in Scientific Machine Learning11th Floor Lecture Hall
- Speaker
- Karthik Duraisamy, University of Michigan
- Session Chair
- George Karniadakis, Brown University
Abstract
This talk will review some recent developments in scientific machine learning, and attempt to offer a structured perspective on the current, somewhat chaotic landscape from the perspective of Industrial problems. Following this, we will discuss the synergistic integration of physical and mathematical structure within machine learning models, touching upon 3 aspects : a) Use of conditional parameterization to enforce numerical consistency in mesh agnostic deep learning of spatio-temporal fields; b) Score-based diffusion models that are physically consistent with known physical laws; and c) Learning of operators that have stability guarantees.
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3:20 - 3:50 pm EDTCoffee Break11th Floor Collaborative Space
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3:50 - 4:20 pm EDTPhysics Constrained Machine Learning for Scientific Computing11th Floor Lecture Hall
- Virtual Speaker
- Danielle Robinson, Amazon Web Services AI Labs
- Session Chair
- George Karniadakis, Brown University
Abstract
In this talk, we discuss the development of physically-constrained machine learning (ML) models that incorporate techniques from scientific computing for learning dynamical and physical systems with applications in epidemiology and fluid dynamics. We first study the lack of generalization of black-box deep learning models for ODEs with applications to COVID-19 forecasting and the need for incorporation of advanced numerical integration schemes. We then focus on learning a physical model that satisfies conservation laws which are ubiquitous in science and engineering problems ranging from heat transfer to fluid flow. Violation of these well-known physical laws can lead to nonphysical solutions. To address this issue, we propose a framework, which constrains a pre-trained black-box ML model to satisfy conservation by enforcing the integral form from finite volume methods. We provide a detailed analysis of our method on learning with the Generalized Porous Medium Equation (GPME), a widely-applicable parameterized family of PDEs that illustrates the qualitative properties of both easier and harder PDEs. Our model maintains probabilistic uncertainty quantification (UQ), and deals well with shocks and heteroscedasticities. As a result, it achieves superior predictive performance on downstream tasks, e.g., shock location detection. Lastly, we study how to hard-constrain Neural Operator solutions to PDEs to satisfy the physical constraint of boundary conditions on a wide range of problems including Burgers’ and the Navier-Stokes’ equations. Our model improves the accuracy at the boundary and better guides the learning process on the interior of the domain. In summary, we demonstrate that carefully and properly enforcing physical constraints using techniques from numerical analysis results in better model accuracy and generalization in scientific applications.
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4:30 - 5:00 pm EDTTBA11th Floor Lecture Hall
- Speaker
- Somdatta Goswami, Johns Hopkins University
- Session Chair
- George Karniadakis, Brown University
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5:10 - 6:40 pm EDTReception11th Floor Collaborative Space
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