Our Dagstuhl Seminar aims to bring together leading experts in mathematical, computational, and biomedical and medical imaging sciences with research interests in data science, machine learning, modeling, optimization, and (statistical) inversion with applications in (but not limited to) medical imaging, and in particular oncology. A central theme of our seminar is the integration of data-driven methods (i.e., machine learning) with model-driven approaches (e.g., biophysical priors and statistical inversion) for predictive modeling. We hypothesize that this integration allows us to (a) augment the available data for training, (b) achieve more generalizable data-driven models, and (c) yield results that are more interpretable.

The seminar has four main thrusts: (i) machine learning in the context data analytics and data-driven model prediction, (ii) predictive computational modeling through (statistical) inversion, (iii) integration of machine learning with model-based priors, and (iv) use of these methods to aid decision making (e.g., in our fight against cancer). We want to discuss these topics through the lens of foundational algorithmic complications, and mathematical and computational challenges, and explore how advances in the applied sciences (e.g., data analytics, medical imaging, radiomics, genomics, or experimental design) can aid us to tackle these challenges.

The overarching issues are robustness of computational methods, generalizability, reproducibility, reliability, algorithmic complexity, performance optimization, shared and distributed memory parallelization, mixed-precision algorithms, scalability, hardware acceleration, software deployment (in parallel / hybrid computing architectures), augmentation of data, and software premises for developing open-source packages for the research community at large. Our premise is to compare performance in terms of a holistic view, including theoretical properties, runtime efficiency, and parallel scalability, but also sustainability and suitability for energy-efficient and comparably cheap accelerator hardware such as graphics processing units.

In the context of predictive computational modeling and statistical inversion, we plan to address topics ranging from uncertainty quantification, model choices (multiscale versus macroscopic; model-complexity; multispecies versus single-species), regularization strategies, sensitivity analysis, strategies to address the massive computational costs (e.g., reduced-order modeling, sampling strategies, optimization algorithms), challenges in the design of hardware-accelerated computational methods with optimal energy efficiency, and strategies to yield the throughput, robustness, and reliability required in practical applications under given hardware constraints. In the context of machine learning and its integration with predictive modeling and priors, we want to cover topics ranging from (stochastic) algorithms for non-convex optimization, regularization strategies, issues with limited reproducibility beyond the training data, robustness against outliers, issues with small-sample size problems (e.g., how to reliably train complex networks), uncertainty quantification for learning from data through the lens of models under data and model uncertainty, model-based data augmentation for data-driven approaches, data augmentation to alleviate issues with reliability and generalizability, and generic strategies to enrich the available data. Lastly, we intend to identify new imaging avenues that can help to (i) provide a better data basis for predictive modeling, (ii) trigger community efforts to enrich available data, and (iii) enable validation and to standardize population-based studies. We want to address reproducibility issues, given that in many cases (medical imaging) data is proprietary. We plan to discuss the significant challenges associated with the validation of the proposed methodology, and a lack of reproducibility due to the absence of standard protocols for validation of data- and model-driven methods by translational research groups (in clinical oncology).

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George Biros, Andreas Mang, Miriam Mehl, and Björn H. Menze