Bauhaus
Spring
School
12/03 – 21/03/2026

From FEM to Neural Operators: Scientific Machine Learning for Computational Mechanics.

From FEM to Neural Operators: Scientific Machine Learning for Computational Mechanics

This blended workshop introduces advanced engineering students to a powerful new paradigm in computational mechanics: scientific machine learning. Traditionally, the finite element method (FEM) has been the workhorse for solving partial differential equations (PDEs) in physics and engineering. In this course, we contrast FEM with emerging deep learning-based methods - such as physics-informed neural networks (PINNs), neural operators, and AI-assisted tooling - to give participants a rich, comparative understanding of both frameworks.

The course begins with a self-paced online module with pre-recorded sessions that refreshes core FEM concepts, sets up coding environments (Matlab/PyTorch), and walks through baseline solver implementations. This will be supplemented by the on-site sessions to build foundational fluency. During the in-person phase, morning lectures will dive into the theoretical underpinnings of scientific machine learning for PDEs, while afternoon sessions will focus on hands-on projects. Participants will extend classical FEM solvers, benchmark them against machine learning surrogates, and explore how large language models can assist in code generation, documentation, and experimentation.

What makes this course exceptional is the emphasis on cross-pollination: using the familiarity of FEM to demystify the neural network-based solvers, and vice versa. The week concludes with short presentations where participants share insights from their experiments, fostering reflection and peer learning.


NOTE:
This course includes an attendance phase in Weimar from March 12 to March 21, 2026.

By the end of this course, participants will:

  • Understand the foundational principles of both traditional finite element methods (FEM) and emerging scientific machine learning approaches for solving PDEs in computational mechanics.
  • Gain fluency in modern AI-based solvers, including physics-informed neural networks (PINNs) and neural operators, with an appreciation of their mathematical structure, capabilities, and limitations.
  • Draw meaningful parallels between FEM and neural network-based solvers to better understand where machine learning augments, complements, or diverges from classical approaches.
  • Develop hands-on coding expertise in Matlab and Python/PyTorch through guided exercises that range from FEM implementation to training and evaluating ML-based surrogates.
  • Learn to benchmark and compare solver performance across accuracy, generalizability, and computational efficiency using structured case studies.
  • Acquire skills in prompt engineering for large language models to support rapid prototyping, code explanation, and documentation workflows.


Participants will leave the course with the theoretical understanding and practical experience needed to critically evaluate and implement solver strategies - both classical and machine-learned - for real-world problems in computational mechanics. ain a comprehensive understanding of the intersection of technology, art, and posthuman concepts. Whilst understanding the ability to  critically evaluate the effects of AR might have on our present. After the course, and practically speaking, participants will have learnt how to build and produce artistic augmented works with TikTok Effect House, with hands-on workshops. They will have acknowledged how to guide their individual viewpoints and the theoretical influences, that their works can raise critical questions and opinions on where and how our post-human present is radically/ethically changing our technological understanding of our future and past.

Master’s and PhD students in civil / mechanical / aerospace engineering, applied mathematics or related computational sciences. 

Dr.-Ing Jorge Alberto Lopez Zermeno

2022 – PhD at the Faculty of Civil and Environmental Engineering at Bauhaus University Weimar, specialized in Computational Mechanics.

Since 2021 – Scientific Assistant at the Institute of Structural Mechanics of the Faculty of Civil and Environmental Engineering at the Bauhaus University Weimar, teaching lectures and seminars in the fields of Structural Mechanics and Finite Element Methods.

He has actively taken part in further trainings to improve his qualifications not only in computational mechanics and numerical methods, but also in developing teaching skills and the use of novel AI tools for supporting teaching and research.

 

Your application should be submitted until November 2nd, 2025

Required application documents:

  • Letter of Nomination (applicants financed by the BIP scholarship from the partner universities)
  • CV
  • Letter of motivation or a short motivation video (max. 1min)
  • Portfolio
  • English language certificate (test certificate or a letter from your university stating your English language knowledge)

 

The course fee is 300 EURO and includes:

  • Orientation & Support
  • Programme according to description
  • Teaching materials
  • Certificate
  • Free use of library

 

The course fee does not include:

  • Travel costs
  • Accommodation
  • Insurance
     

Participants, coming from the partner universites in the framework of Erasmus BIP scholarship and BUW students don't pay the course fee.

In addition to the Spring School courses, we offer a comprehensive "Service Package", which includes participation in the excursions and social programme, free entrance to the museums, shuttle-service on the day of arrilval and lunch (from Mon - Fri) in the student cafeteria. The booking of the Service Package for €70 is optional.
 
Students who do not take up the Service Package are automatically required to pay a course deposit of €100. This is to protect us against costs incurred by non-participation. Since in this case, the universities will not receive any funding from the European Commission. The deposit will be refunded as soon as the participants start the course in Weimar.

Please note our terms and conditions (admission conditions, cancellation conditions etc.)
 

3 ECTS
BUW students: please check with the academic programme coordinator for credit recognition.

Explore a new paradigm in computational mechanics - learn how scientific machine learning complements and extends the finite element method.

BLENDED-Course

Part I: Online Phase
t.b.c.

Part II: on site in Weimar
12 March – 21 March 2026

3 ECTS

Language

The course language is English.

BIP ID/Component Code: 
t.b.c.