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Multifidelity methods predict energies of organic molecules with coupled cluster accuracy

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V. Vinod, D. Lyu, M. Ruth, U. Kleinekathöfer, P. R. Schreiner, and P. Zaspel. Predicting molecular energies of small organic molecules with multifidelity methods. J. Comput. Chem., 46: e70056, 2025. DOI:  https://doi.org/10.1002/jcc.70056; also available as chemrxiv-2024-9zz16.

Multifidelity methods for quantum chemistry (QC) is an effective machine learning (ML) tool to reduce computational costs without compromising on model accuracy. In this work, V. Vinod et al. assess the efficiency of several multifidelity methods in predicting energies of small organic molecules with coupled cluster triples (CCSD(T)) accuracy. In addition to an analysis of time-cost and model accuracy, the trained multifidelity models are used to predict CCSD(T) energies for a collection of atmospherically relevant molecules and highly conjugated molecules with high accuracy. This work is associated with the SPP 2363 on “Utilization and Development of Machine Learning for Molecular Applications – Molecular Machine Learning funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under its special priority program scheme.

Multifidelity data hierarchy study for excitation energies shows promising results for application of machine learning methods

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V. Vinod and P. Zaspel. Investigating Data Hierarchies in Multifidelity Machine Learning for Excitation Energies. J. Chem. Theory Comput, 21, 6, 3077–3091, 2025. DOI: 10.1021/acs.jctc.4c01491; also available as arXiv:2410.11392.

Multifidelity machine learning (MFML) has shown to reduce the time-cost of generating training data for machine learning (ML) models used in predicting quantum chemistry (QC) properties. MFML achieves this by using training data from different accuracies, or fidelities. In this work, Vivin Vinod and Peter Zaspel investigate the effect of the multifidelity data hierarchies on the model cost and accuracy. With a new error metric, the error contours of MFML, the work systematically studies the impact of the different fidelities on the overall model error. Based on this outcome, a new multifidelity approach, the Γ-curve is implemented and shown to be a highly efficient method resulting in low model error with as little as two training samples at the costliest fidelity.

Open PhD position in structure-preserving scientific machine learning for port-Hamiltonian ODEs and DAEs

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Are you interested in developing novel scientific machine learning models for a special class of ordinary and differential algebraic equations? We are currently looking for a PhD candidate that supports us in developing Gaussian processes based models with structure preservation in port-Hamiltonian systems.

A PhD position is currently available in the Collaborative Research Center 1701 “Port-Hamiltonian Systems” at University of Wuppertal, Germany. Details on the CRC 1701 and the position can be found here: https://phi.uni-wuppertal.de/en/port-hamiltonian-institute/crc-1701/

The underlying project is under supervision of Prof. Dr. Peter Zaspel and Prof. Dr. Michael Günther. The team of Prof. Peter Zaspel is located at Bergische Universität Wuppertal. The international team focuses on methods development in machine learning, uncertainty quantification and high performance computing with context of applications from the natural sciences, engineering and beyond. It is embedded in the research group on Scientific Computing and High Performance Computing. For more details, see https://www.peter-zaspel.de/ and https://hpc.uni-wuppertal.de. Prof. Dr. Michael Günther is professor in the Applied and Computational Mathematics group. His research focuses on time integration methods for all types of (coupled) dynamical systems, with a focus on port-Hamiltonian ODEs, DAEs and PDEs with applications ranging from Computational Physics, Computational Finance to Computational Electronics. For more details see https://acm.uni-wuppertal.de/de/ .

A successful applicant is expected to have a Master’s degree (or equivalent) in mathematics, computer science, physics, or related field. Sound knowledge in (scientific) machine learning, and knowledge in numerical analysis and numerical linear algebra are expected. Knowledge in parallel programming is desirable. Prior knowledge in differential-algebraic equations, Gaussian processes or kernel based methods is a plus; programming experience in Python or C/C++ is expected. A good command of English is essential, both as the local working language and because of international collaborations. We look for a competent personality with initiative and commitment, who has the ability to work independently and in collaborations.

We offer a 3 year PhD position. The salary will be paid in accordance with the collective agreement for the public service of the German Länder (Tarifvertrag des öffentlichen Dienstes der Länder, TV-L), with salary level 13 (75%). The place of employment will be Wuppertal, Germany.

The position is available immediately. The call for applications is open until April 8, 2025. For further information and in order to apply, please visit the online jobs portal https://stellenausschreibungen.uni-wuppertal.de . There, you will find the official job description and the link for submitting the application material under reference number 25063. If you have questions on the submission process or have questions on the position please contact Prof. Peter Zaspel via zaspel(at)uni-wuppertal.de.

New development in multi-fidelity machine learning methods opens up possibilities for the use of heterogeneous data for the prediction of quantum chemical properties

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V. Vinod and P. Zaspel. Assessing non-nested configurations of multifidelity machine learning for quantum-chemical properties. Machine Learning: Science and Technology, 5, 045005, 2024. DOI: 10.1088/2632-2153/ad7f25; also available as arXiv:2407.17087.

Multi-fidelity methods in machine learning (ML) of quantum chemistry (QC) properties have made high accuracy low cost models more accessible to the community. These have been used in application for a range of properties including excitation energies. Most multi-fidelity methods usually require a nested configuration of the training data, that is, calculations for a geometry are to be made at the lower fidelities as well as the higher fidelities. 
In a recent work, available as a preprint the authors, Vivin Vinod and Peter Zaspel assess a non-nested configuration of multi-fidelity machine learning (MFML) and optimized MFML (o-MFML) methods. Preliminary results suggest that while MFML would still require a nested data structure, o-MFML can generalize reasonably well over a non-nested training data structure. That is, o-MFML opens up avenues for the use of heterogeneous datasets reducing the requirement to make costly calculations for high-fidelity data.

Dataset of diverse quantum chemical properties to enable research and benchmarking of multifidelity machine learning models released!

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VinoV. Vinod, and P. Zaspel. QeMFi: A Multifidelity Dataset of Quantum Chemical Properties of Diverse Molecules. Sci Data 12, 202, 2025. DOI:https://doi.org/10.1038/s41597-024-04247-3; also available as arXiv:2406.14149.

V. Vinod and P. Zaspel. QeMFi: A Multifidelity Dataset of Quantum Chemical Properties of Diverse Molecules (1.1.0) [Data set]. Zenodo. 2024. https://zenodo.org/records/13925688.

With research booming in the field of multifidelity methods for Quantum Chemistry (QC), it becomes important to benchmark the various methods in interest of meaningful comparison of the models. This allows for expedited research by setting standards which subsequent research assess with their own methodological developments. In interest of such a uniform comparison, the Quantum chemistry MultiFidelity (QeMFi) dataset was distributed to the community on an open source CC-BY-4.0 license. Containing 135k geometries of diverse and chemically complex molecules taken from the WS22 database, the QeMFi datatset contains QC properties ranging from excitation energies to molecular dipole moments. For each property, five fidelities of properties are provided with DFT accuracy. The fidelities themselves are formed on the basis set choice. This dataset is a major step in the direction of research and development of multifidelity machine learning methods for QC.

The authors of this work are Vivin Vinod and Peter Zaspel.

Optimal Combination with Multifidelity Machine Learning Achieves Coupled Cluster Accuracy

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Vinod, V., Kleinekathöfer, U., & Zaspel, P. (2024). Optimized multifidelity machine learning for quantum chemistry. Machine Learning: Science and Technology, 5(1), 015054 http://doi.org/10.1088/2632-2153/ad2cef.

Recent research in Multifidelity Machine Learning (MFML) has resulted in ML methods that reduce the cost of generating a training set without compromising on the accuracy of the predictions. This is achieved by the combination of cheaper and less accurate data with high accuracy (or fidelity) and high cost data. In this work, a novel methodological improvement of MFML is benchmarked for various quantum chemical (QC) properties. Optimized MFML (o-MFML) performs the combination of the different fidelities of data are using an Optimal Combination method. With this improvement, it is shown that high accuracy methods such as Coupled Cluster Singlets Double (Triplet) are now more accessible that ever to the ML-QC community. The work is available in the Machine Learning: Science and Technology journal from IOPScience and is authored by Vivin Vinod, Ulrich Kleinekathöfer, and Peter Zaspel.

Reducing Compute Costs of Generating Training Data for Excitation Energy Prediction Using Multifidelity Methods

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Vinod, V., Maity, S., Zaspel, P., & Kleinekathöfer, U. (2023). Multifidelity machine learning for molecular excitation energies. Journal of Chemical Theory and Computation, 19(21), 7658-7670 https://doi.org/10.1021/acs.jctc.3c00882.

A major challenge to accurate predictions of quantum chemical (QC) properties with machine learning methods is the lack of high accuracy data. Generating high accuracy training data for machine learning (ML) is computationally expensive. With the multifidelity machine learning (MFML) method, cheaper and less accurate data is used alongside very little high accuracy data to result in a model with better accuracy in predicting high fidelity data. In this work, the MFML method is benchmarked for vertical excitation energies, a QC property vital to understanding elementary life processes such as photosynthesis. Numerical results indicate a time benefit over a factor of 30. This is a strong step towards development of ML methods for QC reducing the compute cost of generating a training set. This work is authored by Vivin Vinod, Sayan Maity, Peter Zaspel, and Ulrich Kleinekathöfer and has been published in the Journal of Chemical Theory and Computation.

Up to two open PhD positions in numerical methods for large-scale training of Gaussian processes

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Up to two open PhD positions in numerical methods for large-scale training of Gaussian processes

Are you interested in developing new numerical methods for training of machine learning models on large to huge data sets? We are currently looking for PhD candidates that support us in breaking the barriers of computational complexity of Gaussian processes and kernel-based machine learning models.

Up to two PhD positions are available in the team of Prof. Peter Zaspel at University of Wuppertal, Germany. The positions are focused on the development of novel (numerical) methods with fast implementations that help to break the computational complexity in the training of Gaussian processes and kernel-based machine learning models. Depending on the candidate’s interest, a stronger focus can be put on the methods development in fast matrix approximations (e.g. hierarchical matrices, low-rank methods, sparse GPs, etc.) or on the fast implementation on GPUs, i.e. hardware-aware numerics and parallelization.

The team of Prof. Peter Zaspel is located at Bergische Universität Wuppertal. The international team focuses on methods development in machine learning, uncertainty quantification and high performance computing with context of applications from the natural sciences, engineering and beyond. It is embedded in the research group on Scientific Computing and High Performance Computing. For more details, see https://www.peter-zaspel.de/ and https://hpc.uni-wuppertal.de.

A successful applicant is expected to have a Master’s degree (or equivalent) in computer science, mathematics, physics, data science or similar discipline, strong analytical skills in context of machine learning and/or (numerical) mathematics, very good to excellent proficiency in a programming language (preferable Python or C/C++) and interest in developing novel training methods for kernel-based / Gaussian Process machine learning. Experience in matrix approximation techniques or hardware-aware programming on GPUs is an advantage. A good command of English is essential, both as the local working language and because of international collaborations. We look for a competent personality with initiative and commitment, who has the ability to work independently and who enjoys teaching (support).

We offer a 3 year PhD position. The salary will be paid in accordance with the Collective Agreement for the Public Service of the Federation (Tarifvertrag des öffentlichen Dienstes, TVöD Bund), with salary level 13 (75%). The position has teaching (support) duties. The place of employment will be Wuppertal, Germany.

The positions are available immediately and applications will be considered on a rolling basis, but not later than until July 15, 2024. In order to apply, please submit a letter of motivation, a CV, copies of transcripts and optionally a copy of your MSc thesis (all as one PDF). If you you would like to apply or have questions on the position please contact Prof. Peter Zaspel via zaspel(at)uni-wuppertal.de.

Expired: PhD position in large-scale GPU-based training in molecular machine learning

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Are you interested in developing new machine learning training methods for large to huge data sets and have strong programming skills ideally on GPUs, then apply for our just opened PhD position!

A PhD position is available in the team of Prof. Peter Zaspel at University of Wuppertal, Germany. The position is focused on the development of novel machine learning training algorithms on GPUs in context of molecular simulations for materials design under the project “Multi-fidelity methods for fast large-scale mixed-precision molecular machine learning on GPUs”. The respective research will involve the further development of large-scale machine learning models and hardware-aware algorithms in an interdisciplinary application.

The team of Prof. Peter Zaspel is located at Bergische Universität Wuppertal. The international team focuses on machine learning, uncertainty quantification and high performance computing in context of applications from the natural sciences, engineering and beyond. It is embedded in the research group on Scientific Computing and High Performance Computing. For more details, see https://www.peter-zaspel.de/ and https://hpc.uni-wuppertal.de.

A successful applicant is expected to have a Master’s degree (or equivalent) in computer science, mathematics, physics, data science or similar discipline, strong analytical skills in context of machine learning and/or (numerical) mathematics, excellent proficiency in a programming language (preferable Python or C/C++) and interest in developing novel, hardware-aware training methods on GPUs in context of kernel-based / Gaussian Process machine learning for simulation applications. Experience in hardware-aware programming on GPUs or parallelization of algorithms is an advantage. A good command of English is essential, both as the local working language and because of our international collaborations. We look for a competent personality with initiative and commitment, who has the ability to work independently and who enjoys teaching (support).

We offer a 3 year PhD position. The salary will be paid in accordance with the Collective Agreement for the Public Service of the Federation (Tarifvertrag des öffentlichen Dienstes, TVöD Bund), with salary level 13 (75%). The position has teaching (support) duties. The place of employment will be Wuppertal, Germany.

The position is available immediately and applications will be considered until January 22, 2024. Applicants have to use the online portal of the University of Wuppertal https://stellenausschreibungen.uni-wuppertal.de, where the job offer is available under the ID 23417. There, you need to submit a letter of motivation, a CV, copies of transcripts and optionally a copy of your MSc thesis (all as one PDF). International applicants should switch to the English version of the web page via the flag symbol on the top of the page. Then, applicants will find the row with the above given ID and click on “Jetzt bewerben” on the right-hand side of that row. The remaining process is available in English. If you have questions on the position or with respect to the application process please contact Prof. Peter Zaspel via zaspel(at)uni-wuppertal.de.

Neuer Experte will innovative Forschungs-Software entwickeln

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Peter Zaspel ist neuer Professor für Software für datenintensive Anwendungen an der Bergischen Universität Wuppertal.

Forschende in Wissenschaft und Technik arbeiten mit großen Datenmengen. Diese beinhalten Messungen, Simulationen und Kombinationen hiervon, wofür eine umfangreiche IT-Infrastruktur nötig ist. Die Entwicklung von effizienter und erweiterbarer Software sowie von Methoden für datenintensive Anwendungen in den Naturwissenschaften, der Technik und darüber hinaus ist das Ziel der Forschungsarbeit von Peter Zaspel. Anwendungsfelder solcher Programme können zum Beispiel Quantenchemie, Klimarekonstruktion und Medikamentenforschung sein.

Please find the full press release here.