Scientific Training II

Data-Driven Modeling of Mechanical Systems

Madrid, 8-11 April 2019

PhD course on data driven modelling of mechanical systems. Including parameter estimation from imaging as well as numerical optimization methods. Experts in the field will cover simulation and optimization basics, followed by multiple methodologies to incorporate data-specific knowledge into simulation methods: measurement-based parameter estimation, design of subspace and coarsened models, and learning-based data-driven simulation methods.

Course content

As part of personalized clinical design, it is essential to develop simulation tools that adapt to the particular properties and condition of each patient. This is possible through the acquisition of patient-specific data, and tuning of simulation models and parameters to match the observations in the data. Out of the many properties and phenomena that can be modeled in a data-driven manner, this course focuses on mechanical behavior. Even then, there are multiple ways in which data can be exploited in the design of personalized simulation models, and these course explores several of these ways.

One way is to set up a generic model, and estimate particular parameters that produce a personalized instance of the model. We refer to this methodology as measurement-based parameter estimation or parameter identification. The input data must include several observations of patient deformations, and the estimation of parameters is formulated as an optimization problem. Typically, this optimization must also fulfill mechanical constraints that ensure the biomechanical validity of the problem.

Another way to account for data is to devise a very accurate and high-resolution simulation model, and then leverage precomputation of simulation data to reach a more efficient simulation model. This second model can be used, perhaps interactively, in the context of design tasks. The course visits two types of approaches to precompute fast data-driven simulation models. One approach is the use of global subspace methods, and the other approach is the use of numerical coarsening methods. Both approaches try to find a complex but compact basis that represents well the richness of full simulations, and they differ in the properties of the basis and hence the precomputation method.

The last way to account for data is to follow modern machine learning approaches, which model complex input-output functions through many combinations of local linear and nonlinear operators. Deep learning techniques have demonstrated success at reproducing very complex phenomena through the discovery of meaningful latent spaces. The course will cover the basics of deep learning and its application to modern mechanical simulation problems.

Before addressing the major data-driven modeling techniques, the course will cover basics of the two main tools that will be used in combination: simulation principles and numerical optimization.

Learning objectives

• Understand the basics of simulation of mechanical systems, discretization and solvers.
• Understand the basics of numerical optimization, objective functions, constraints, and solvers.
• Develop measurement-based estimation procedures through constrained optimization.
• Develop subspace simulation models based on precomputed data.
• Develop machine learning models for mechanical simulation problems.

Program

Monday April 8
9:30 – 11:00 Presentation and introduction to simulation of mechanical systems
11:00 – 11:30 break
11:30 – 13:00 Development of an example mechanical simulation solver
13:00 – 14:00 lunch break
14:00 – 15:30 Introduction to numerical optimization
15:30 – 16:00 break
16:00 – 17:30 Test and refinement of optimization approaches

Tuesday April 9
9:30 – 11:00 Basics of model estimation through optimization
11:00 – 11:30 break
11:30 – 13:00 Implementation of basic parameter estimation algorithm
13:00 – 14:00 lunch break
14:00 – 15:30 Implementation of a refined parameter estimation algorithm
15:30 – 16:00 break
16:00 – 17:30 Tour of the Multimodal Simulation Lab

Wednesday April 10
9:30 – 11:00 Introduction to subspace simulation methods
11:00 – 11:30 break
11:30 – 13:00 Implementation of a subspace simulation solver
13:00 – 14:00 lunch break
14:00 – 15:30 Introduction to numerical coarsening methods
15:30 – 16:00 break
16:00 – 17:30 Invited talk: Nils Thuerey, TU Munich

Thursday April 11
9:30 – 11:00 Introduction to neural networks
11:00 – 11:30 break
11:30 – 13:00 Application of neural networks to simulation problems
13:00 – 14:00 lunch break
14:00 – 15:30 Advanced applications of deep learning in simulation 

System and software prerequisites

All participants should use their own laptop, with the following installation:

• Operating system: Windows 10/8/7 (or another recent version).
• Software:
• Unity3D: Download the installer for Windows.
• Visual Studio Community 2017: Installed with Unity3D.
• Python 3 + Anaconda: During the installation of Visual Studio, modify the settings and select Python Tools.

Course material

All course material provided to participants on site.

Speakers