ENWAT Project
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Publication date: Sep 4, 2024
| Position-ID: | 1583 |
| Faculty/ Facility: | Civil- and Environmental Engineering |
| Institute/ Facility: | Civil- and Environmental Engineering : IWS – Institute for Modelling Hydraulic and Environmental Systems |
| Research Association: | N/A |
| Teaching Obligation: | No |
| Application deadline: | 10/31/2024 |
| Anticipated Start Date: | 10/01/2025 |
About Us
The international Doctoral Program “Environment Water” (ENWAT) of the Faculty of Civil and Environmental Engineering Sciences, University of Stuttgart, Germany, in collaboration with the German Academic Exchange Service (DAAD) opens a call for max. 2 PhD positions for research in Environment Water. Each project involves high-quality research and state-of-the-art techniques and is supervised by excellent researchers. We are looking for highly motivated and talented students with a passion for science. Candidates must demonstrate an excellent performance in their previous academic education.
Title: Deep Chaos ODE for Advanced Hydrological Modelling: Integrating Deep Learning and Polynomial Chaos into Data-Driven Hydrology
Advisor: Prof. Dr.-Ing. Wolfgang Nowak, apl. Prof. Sergey Oladyshkin, Dr. rer. nat. Jochen Seidel
Research group / department:
Chair of Stochastic Simulation and Safety Research for Hydrosystems (LS3)
Institute for Modelling Hydraulic and Environmental Systems (IWS)
Stuttgart Centre for Simulation Technology (SC SimTech)
Keywords: Hydrological modelling, Model development, Deep learning, , arbitrary Polynomial chaos, Mass balance, Data-driven modeling
Introduction / Background
The majority of hydrological models rely heavily on the principle of mass balance, often represented through Ordinary Differential Equations (ODEs). These models encapsulate the conservation of mass within hydrological systems, ensuring that the inflows, outflows, and storage changes are accurately accounted for. This fundamental principle, coupled with assumed relationships between various components of the hydrological cycle (such as precipitation, evapotranspiration, runoff, and infiltration), forms the core of traditional hydrological modeling approaches. However, these assumed relationships, often coded as linear forms, do not offer the flexibility needed to capture the non-linear and dynamic interactions present in real-world hydrological systems.
Lately, there has also been the branch of neural hydrology, where hydrological models are directly learned from data via machine learning (e.g., LSTM neural networks, [1]). Initially, these models ignored all physical background knowledge and did not necessarily conserve mass, as they used black-box model structures far away from that of rainfall-runoff models. For these reasons, neural hydrology is often criticized by the conventional hydrological community. Alternatively, it is well known that Neural ODEs [2] are capable of representing dynamic systems that are coded in ODEs. They can encapsulate the complex temporal dependencies and dynamics inherent in hydrological systems, offering a promising direction for integrating machine learning with physical modeling. The potential of neural ODE models in hydrology has been discussed in [3].
However, long-term predictions using Neural ODEs may not be reliable for highly nonlinear systems due to the mathematical structure of the involved neural networks. Recent research in our department has demonstrated that arbitrary Polynomial Chaos ODEs (Chaos ODEs), which utilize the orthonormal decomposition of aPC [4], outperform Neural ODEs and as well Gaussian Process Emulator ODEs in terms of accurately capturing the complexity of dynamic processes. Moreover, further extension of Chaos ODEs to Deep Chaos ODEs by using Deep arbitrary Polynomial Chaos Neural Networks (DaPC NN, [5]) may offer significant additional advantages: By combining polynomial chaos expansion with neural network structures, the DaPC NN is more flexible in modelling higher-order interactions, while performing better in predictions outside the available training data.
Your Tasks
Research goals:
Our primary goal is to improve the accuracy and prediction reliability of hydrological models. Hence, we propose methodological research to exploit Chaos ODEs for hydrological modelling, and to develop the concept of Deep Chaos ODE. By doing so, we seek to allow for the model flexibility that made neural hydrology so successful, while maintaining the fundamental mass balance relationships and while utilizing hydrological knowledge even in machine-learned models.
Additionally, following the recent advances of aPC, the framework could be extended to include Bayesian, sparse, and other features, providing a versatile and powerful toolset for various modeling scenarios. This new approach offers a unique perspective, enabling us to uncover hidden patterns and dependencies within hydrological systems, thereby advancing both theoretical understanding and practical applications.
Methods to be used:
The research will explore system-specific architectures of deep learning, focusing on the formulation suggested in [2] and the structure in [5], resulting in the desired Deep Chaos ODEs. These methodologies will be employed to model dynamic systems, where the dependencies between state variables and their temporal evolution will be learned. State variables will be defined similarly to those in existing conceptual hydrological rainfall-runoff models, such as HBV. However, the storage terms and fluxes, as functions of the current model states, will be learned using Deep Chaos ODE, which inherently follows the principle of mass balance.
To validate and test the proposed framework, selected case studies will be implemented and compared against suitable baseline models, such as standard HBV and traditional neural hydrological models. The selection of methods and case studies will be tailored to identify the most effective combination for addressing the challenges posed by the proposed research. This methodological flexibility is crucial for optimizing the model’s performance and ensuring its applicability to real-world hydrological systems. The Deep Chaos ODE approach aims to provide a more accurate and robust representation of the underlying processes, offering significant improvements over existing methods.
References:
[
[1]. Kratzert, F., Klotz, D., Brenner, C., Schulz, K., & Herrnegger, M. Rainfall–runoff modelling using long short-term memory (LSTM) networks. *Hydrology and Earth System Sciences*, 22(11), 6005-6022. (2018).
[2]. Chen, R. T., Rubanova, Y., Bettencourt, J., & Duvenaud, D. K. Neural ordinary differential equations. *Advances in Neural Information Processing Systems*, 31. (2018).
[3]. Höge, M., Scheidegger, A., Baity-Jesi, M., Albert, C., & Fenicia, F. Improving hydrologic models for predictions and process understanding using neural ODEs. *Hydrology and Earth System Sciences*, 26(19), 5085-5102. (2022).
[4]. Oladyshkin, S., & Nowak, W. Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion. *Reliability Engineering & System Safety*, 106, 179-190. (2012).
[5]. Oladyshkin, S., Praditia, T., Kroeker, I., Mohammadi, F., Nowak, W., & Otte, S. The deep arbitrary polynomial chaos neural network or how Deep Artificial Neural Networks could benefit from data-driven homogeneous chaos theory. *Neural Networks*, 166, 85-104. (2023).
Your Profile
Prerequisites:
- MSc in hydrology, environmental sciences, hydrogeology, water management (or similar) or in data sciences, statistics, applied mathematics.
- Skills in programming (e.g. python, matlab, julia)
- Skills at scientific writing and presentation
- Ability to work independently and in a team
- Willingness to learn new concepts and methods
- Experience (e.g., coursework, thesis work) in hydrological modelling or in machine learning is desirable
- Willingness to contribute to the goals and culture of the research group
Further Prerequisites:
- Resume/CV showing the applicant’s background, professional skills, a list of publications and oral and poster presentations as well as additional achievements (scholarships, awards etc.)
- M.Sc., Dipl.-Ing. or equivalent degree in Civil Engineering, Water Resources Management, Environmental Engineering or related sciences
- B.Sc. in Civil Engineering, Water Resources Management, Environmental Engineering or related sciences
Copies of Certificates and Transcripts, including all undergraduate level certificates and university degrees. All documents, which are not in English or in German, must be accompanied by copies of a legally certified English translation (for the application we will accept copies; but please be aware, that originals or legally certified copies will be needed for the final phase. In case any differences between the copies and the originals show up, the application will be dismissed.)
Please make sure, that the copies of the transcripts show not only the grades but also explain the home grades’ system (please add copy of the description of grade scale).
- At the time of application, generally no more than 6 years should have passed since the last degree was gained.
- Only international (non-German) applicants can be accepted. At the time of application the candidate must not have been resident in Germany for more than the last 15 months.
- Unless native speaker: proficiency in English (e.g. TOEFL, IELTS, etc.), or proof that M.Sc. and B.Sc. programs were held in English.
- 2 Reference letters from university professors from the applicants home university, issued during the last 2 years.
- Motivation letter describing the applicant’s work experience and research goals (1 page).
Your Benefits
Research Environment:
This research will be embedded into the Chair of Stochastic Simulation and Safety Research for Hydrosystems (LS3) at the IWS, Faculty of Civil and Environmental Engineering. Depending on qualification of the candidate, a formal association of the project to the SC SimTech and the Cluster of Excellence in Data-Integrated Simulation Science is possible and advisable.
Employment and compensation information
Maximal Funding Period or Duration of Employment: 48 months
Type of Funding: Scholarship
Compensation: 1300 € per month
Percentage of weekly working hours (usually 39.5h = 100%):100%
Employment at the cooperation partner:
Location: Stuttgart, Campus Vaihingen
If Location other than Stuttgart or additional location(s): N/A
Contact Details
Contact person: Dr. Gabriele Hartmann
Mail: gabriele.hartmann@f02.uni-stuttgart.de
Phone: +49 711 685 66585
Website: https://www.iws.uni-stuttgart.de/ls3/
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Women who apply will be given preferential consideration in areas in which they are underrepresented, provided they have the same aptitude, qualifications and professional performance. Severely disabled applicants with equal qualifications will be given priority.
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