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HGS MathComp - Where Methods Meet Applications

The Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences (HGS MathComp) at Heidelberg University is one of the leading graduate schools in Germany focusing on the complex topic of Scientific Computing. Located in a vibrant research environment, the school offers a structured interdisciplinary education for PhD students. The program supports students in pursuing innovative PhD projects with a strong application-oriented focus, ranging from mathematics, computer science, bio/life-sciences, physics, and chemical engineering sciences to cultural heritage. A strong focus is put on the mathematical and computational foundations: the theoretical underpinnings and computational abstraction and conception.

HGS MathComp Principal Investigators are leading experts in their fields, working on projects that combine mathematical and computational methodology with topical research issues. Individual mentoring for PhD candidates and career development programs ensure that graduates are fully equipped to take up top positions in industry and academia.

21.07.2025 - 25.07.2025
09:00 - 14:30
Theory & Methods
Romberg Course: Multilayer Multiconfiguration Time-Dependent Hartree Method
Compact Courses

Speaker: Prof. Haobin Wang • University of Colorado Denver • Romberg Visiting Scholar
Location: Mathematikon • Conference Room, Room 5/104, 5th Floor • Im Neuenheimer Feld 205, 69120 Heidelberg
Registration: Please register here
Organizer: HGS MathComp
ECTS: 2
This course is part of the HGS MathComp Romberg Program.

Target Audience:
Graduate students and researchers in theoretical/computational chemistry, applied mathematics, or related fields.

Prerequisites:
First-year linear algebra, basic differential equations; undergraduate quantum mechanics is helpful, but not required.

Course Format:
5-day intensive course, 3 hours of lecture per morning (split into two 90-minute sessions), 1-hour afternoon recitation session for exercises and discussions. Course times: 9:00-12:30 & 13:30-14:30.

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method—also known in applied mathematics as the (time-dependent) hierarchical Tucker or tree tensor network decomposition—is a powerful variational technique for simulating quantum dynamics in high-dimensional systems. It constructs efficient, recursive, time-adaptive representations of wavefunctions using dynamically contracted tensor networks. This short course introduces the theoretical foundations, numerical formulations, and computational implementations of ML-MCTDH, with emphasis on its application to condensed phase chemical physics. Relevant connections to tensor methods in numerical analysis and data science will also be briefly noted.

Course outline:
1. Standard variational approach to solve time-dependent Schrödinger equations.
(a) Conventional eigenfunction (basis) expansion method to the Schrödinger equations - linear homogeneous PDEs to ODEs.
(b) Variational principle and Dirac-Frenkel framework.
(c) Continuous and grid basis functions, finite basis representation and discrete variable representation, contraction of the basis functions.
(d) Initial conditions and integration schemes.
(e) Scaling issues and motivation for advanced methods.
2. The multiconfiguration time-dependent Hartree (MCTDH) method.
(a) The Heidelberg formulation of the MCTDH method: Tucker decomposition of the full tensor.
(b) Nonlinear equations of motion and projection
(c) Initial condition preparation and numerical propagation; regularization of the equations of motion.
(d) Applications and scaling analysis.
3. The ML-MCTDH method.
(a) Tree tensor networks and multilayer structure.
(b) Recursive equations of motion.
(c) Technical details of the simulations: basis functions, integration schemes, and tree structures.
(d) Models of condensed phase chemistry/physics and specific ML-MCTDH implementations.
(e) Discussion of scaling and numerical challenges.
4. Treating identical particles.
(a) The second quantized representation: dummy encoding and the permutation symmetry/anti-symmetry.
(b) Treating identical fermions: Jordan-Wigner transformation.
(c) Technical considerations and sample applications.
5. Calculating energy eigenstates.
(a) Tree tensor representation for time-independent problems.
(b) Multilayer Improved Relaxation method: Krylov subspace iteration and alternating optimization.
(c) Example applications.
(d) Current limitations and possible extensions.
 
28.07.2025 - 01.08.2025
Practicals & Schools
MCTDH Summer School 2025
School

Location: Hörsaalzentrum Chemie • "Kleiner Hörsaal" • Im Neuenheimer Feld 252 • 69120 Heidelberg
Registration: Please apply on the event website
ECTS: 3
The MCTDH Summer School offers an intensive training program designed to provide participants with hands-on experience using the Heidelberg MCTDH software, as well as theoretical background on the underlying principles and methods, including its multilayer generalization.

The program targets mainly PhD students, early-stage researchers, and aims at providing them with sufficient proficiency to afterward apply the MCTDH method in their day-to-day research activities.

Costs and attendance:
- The attendance to the school is free of charge.
- Coffee breaks and lunch vouchers will be provided.
- Accommodation and extra meals must be organized by the participants themselves.

We can accept only a limited number of participants. For admittance, please follow the instructions on how to apply.
The deadline for applications is April 10, 2025.

Organizers:
Prof. Fabien Gatti • CNRS, University Paris-Saclay, France
Dr. Markus Schröder • Institute of Physical Chemistry, Heidelberg University
Prof. Oriol Vendrell • Institute of Physical Chemistry & IWR, Heidelberg University
Prof. Graham Worth • Department of Chemistry, University College London, England

The school spreads over five days with theory sessions in the morning and hands-on exercises in the afternoon. The list of topics covered includes:

- Numerical methods for quantum dynamics
- MCTDH theory
- Introduction to polyspherical coordinates
- Mode combination and multilayer trees
- Vibronic Hamiltonians for photophysics and photochemistry
- Scattering and molecular dissociation
- High-dimensional problems
- Hands-on exercises with the Quantics / Heidelberg MCTDH package, including
- Spectroscopy & quantum control
- Reactive scattering
- Direct dynamics / GWP
- Practical use of the TANA program for deriving analytical kinetic operators
- Potential energy operators in sum-of-products form
 
01.09.2025 - 05.09.2025
Practicals & Schools
European Conference on Numerical Mathematics and Advances Applications (ENUMATH 2025)
Conference

Speaker: Various Speakers
Location: Heidelberg
Registration: Please register on the event website
ECTS: 2
The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) conferences are a forum for presenting and discussing novel and fundamental advances in numerical mathematics and challenging scientific and industrial applications on the highest level of international expertise.

For more information, please visit the event website.

As members of the University of Heidelberg, those of you who would like to participate can contact us at enumath2025@uni-heidelberg.de to receive a voucher to have the participation fee waived. Note that the voucher is required during the registration process, so make sure you register after having received one.

Conference Themes
• Advances in Discretisation Schemes
• Multiscale and Multiphysics Problems
• Hardware-Aware Scientific Computing
• Inverse Problems
• Uncertainty Quantification 
• Data-Driven Modelling and Simulation
• Scientific Machine Learning
• Reduced Order Models and Surrogates
• Randomised Numerical Algorithms
• Numerical Optimisation and Optimal Control

For more information, please visit the event website.