Modeling, Optimization, and Control

Optimization and control are fundamental to many problems in biomedicine. For instance, in medical interventions, the objective is often to eliminate pathogens efficiently while minimizing adverse side effects. Precision medicine takes this a step further, aiming to tailor treatments to the unique characteristics of individual patients. 

A central aim of the workshop is integrating mechanistic modeling and data-driven insights with optimization and control methods for biomedical applications. In particular, modern automatic differentiation tools—which form the backbone of many AI methods—are also highly valuable for calibrating and controlling complex dynamical systems in biomedicine and beyond.

The first day of the workshop will highlight recent advances in modeling, optimization, and control methods applied across a range of biomedical systems. The second day will be dedicated to exploring the complex interactions between the microbiome and antibiotics. As antibiotic resistance continues to rise, there is a growing need for more targeted and judicious use of these drugs. However, the intricate dynamics of multi-species bacterial ecosystems—and the challenges associated with managing them through antibiotic interventions—make treatment optimization in these contexts particularly demanding.

Workshop dates: August 28 and 29, 2025

Workshop location: Executive Learning Centre (2A), Frankfurt School of Finance & Management (Adickesallee 32–34, 60322 Frankfurt am Main)

August 28^th, 2025 | Room: Executive Learning Centre (2A)

August 29^th, 2025 | Room: Executive Learning Centre (2A)

"Evolution of Structured Populations: From Cells to Organisms" by Tom Chou (University of California, Los Angeles)

Abstract: Multiscale models are needed to more clearly frame the emergence, transmission, and public health aspects of drug resistance. I will present mathematical models that describe competition among different within-host subpopulations, such as wild-type and drug -resistant bacteria, under different conditions (drug treatments). A number of different scenarios can be modeled using different parameter sets, which need to be better identified from clinical and field observations. The clinical implications of antibiotic drug resistance need to be addressed with spatiotemporal population-level models that I will discuss.

"Detection and Suppression of Epileptiform Seizures via Model-Free Control and Derivatives in a Noisy Environment" by Michel Fliess (École Polytechnique)

Abstract: Recent advances in control theory yield closed-loop neurostimulations for suppressing epileptiform seizures. These advances are illustrated by computer experiments which are easy to implement and to tune. The feedback synthesis is provided by an intelligent proportional-derivative (iPD) regulator associated to model-free control. This approach has already been successfully exploited in many concrete situations in engineering, since no precise computational modeling is needed. iPDs permit tracking a large variety of signals including high-amplitude epileptic activity. Those unpredictable pathological brain oscillations should be detected in order to avoid continuous stimulation, which might induce detrimental side effects. This is achieved by introducing a data mining method based on the maxima of the recorded signals. The real-time derivative estimation in a particularly noisy epileptiform environment is made possible due to a newly developed algebraic differentiator. The virtual patient is the Wendling model, i.e., a set of ordinary differential equations adapted from the Jansen-Rit neural mass model in order to generate epileptiform activity via appropriate values of excitation- and inhibition-related parameters. Several simulations, which lead to a large variety of possible scenarios, are discussed. They show the robustness of our control synthesis with respect to different virtual patients and external disturbances.

"Mechanistic Computational Modeling of Malignant Cell Dynamics in the Human Bone Marrow" by Thomas Stiehl (RWTH Aachen and Roskilde University)

The human body produces more than 100 billion blood cells each day. This process, known as hematopoiesis, is highly complex and tightly regulated. It is driven by hematopoietic stem cells (HSCs), which reside in the bone marrow. HSCs can self-renew, meaning they produce identical copies of themselves to maintain the stem cell pool throughout life. At the same time, they can differentiate into progressively more mature cell types that give rise to all lineages of blood cells. As individuals age, HSCs accumulate mutations that can confer a competitive advantage, resulting in clonal expansion. This condition, known as clonal hematopoiesis of indeterminate potential (CHIP), is characterized by a substantial proportion of blood cells originating from a single mutant stem cell clone. CHIP is common in older adults, with a prevalence of up to 30% in individuals over 80 years of age. As CHIP is associated with an increased risk of hematologic malignancies such as acute myeloid leukemia (AML), a quantitative understanding of its progression is urgently required. To investigate the dynamics of clonal expansion in the human bone marrow, we develop mechanistic ordinary differential equation models. The models account for key biological processes including cell proliferation, self-renewal, differentiation, and death. The cell kinetics are subjected to nonlinear feedback loops and micro-environmental cues such as stem cell niche interactions.

By integrating computational modeling with patient data, we aim to address the following questions:

· How do the kinetic properties (proliferation, self-renewal, differentiation) of wild-type and mutated HSCs differ?
· What mechanisms drive the expansion of specific mutant clones, and what role could chronic inflammation play?
· Which stem cell properties govern clonal selection?
· Which mechanisms mediate the disease progression of stem cell-driven malignancies such as acute myeloid leukemia?

"Structured Population Models of Cell Migration Incorporating Membrane Reactions" by Pia Domschke (Frankfurt School of Finance & Management)

The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes enables a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this work we establish a general spatio-temporal-structural framework that enables the description of surface-bound reaction processes coupled with the cell population dynamics. We provide a general theoretical description for this approach and illustrate it with examples arising from cancer invasion.

"Gut Microbial Communities as Complex Systems" by Karoline Faust and Pallabita Saha (KU Leuven)

Our gut microbiome performs a number of important tasks, such as vitamin synthesis, fiber degradation and protection from pathogens, and is involved in multiple diseases. Thus, there is hope to treat gastrointestinal diseases through microbiome-based therapeutics. However, gut microbial communities consist of hundreds of species interacting with each other and their human host, thereby forming complex systems. We study synthetic gut communities in controlled conditions to gain a mechanistic understanding of their interactions and the resulting dynamics. Here, I will illustrate the complex dynamics that can arise from the interactions between gut bacteria with a few examples.

"Hybrid Inference for Microbial Community Models: Physics-Informed Neural Networks for Parameter Estimation in Generalized Lotka-Volterra Systems" by Lorenzo Sala (INRAE Jouy-en-Josas)

Understanding and modeling the dynamics of microbial ecosystems is crucial for advancing microbiome research and supporting biomedical applications such as diagnostics, personalized therapies, and ecosystem engineering. However, parameter estimation from experimental data- often sparse, noisy, and unevenly sampled - poses a major challenge for mechanistic models like the Generalized Lotka-Volterra (GLV) framework. In this work, we introduce a hybrid modeling approach that integrates mechanistic insights with machine learning via Physics-Informed Neural Networks (PINNs). By embedding the GLV equations as soft constraints in the neural network's loss function, our method fuses prior biological knowledge with observational data to enable more robust and interpretable parameter inference. This formulation leverages automatic differentiation to enforce consistency with known dynamics while flexibly accommodating noise, missing values, and irregular sampling. We show that this combination of data-driven learning and mechanistic structure improves the identifiability of key parameters - such as species interaction coefficients and intrinsic growth rates - critical for characterizing microbial behavior and enabling cross-condition comparisons. The resulting PINN model also acts as a differentiable and scalable surrogate, suitable for integration into broader frameworks like digital twins. This work contributes to the broader goal of bridging mechanistic modeling and data-driven inference in biomedicine, illustrating how hybrid approaches can enhance the reliability, interpretability, and generalizability of models for complex biological systems.

"Model-Based Control of Biomedical Dynamical Systems Using Neural Networks and Automatic Differentiation" by Lucas Böttcher (Frankfurt School of Finance & Management)

Abstract: Many engineered systems are intentionally designed to align well with traditional control theory techniques. In contrast, biomedical systems are often high-dimensional, span multiple time and spatial scales, and exhibit stochastic behavior. These features present major challenges for classical control approaches. In this talk, I will discuss how neural networks can be used to parameterize control functions for complex, nonlinear biomedical systems. I will also outline how tools such as automatic differentiation and gradient-free optimization can be employed in biomedical applications. Finally, I will highlight techniques like stochastic differentiation and gradient approximations, which are particularly useful when the system dynamics are non-differentiable or incompatible with standard gradient-based methods.

"Gut microbial communities as complex systems" by Karoline Faust (KU Leuven)

Abstract: Our gut microbiome performs a number of important tasks, such as vitamin synthesis, fiber degradation and protection from pathogens, and is involved in multiple diseases. Thus, there is hope to treat gastrointestinal diseases through microbiome-based therapeutics. However, gut microbial communities consist of hundreds of species interacting with each other and their human host, thereby forming complex systems. We study synthetic gut communities in controlled conditions to gain a mechanistic understanding of their interactions and the resulting dynamics. Here, I will illustrate the complex dynamics that can arise from the interactions between gut bacteria with a few examples.

"Hybrid Inference for Microbial Community Models: Physics-Informed Neural Networks for Parameter Estimation in Generalized Lotka-Volterra Systems" by Lorenzo Sala (INRAE Jouy-en-Josas)

Understanding and modeling the dynamics of microbial ecosystems is crucial for advancing microbiome research and supporting biomedical applications such as diagnostics, personalized therapies, and ecosystem engineering. However, parameter estimation from experimental data- often sparse, noisy, and unevenly sampled - poses a major challenge for mechanistic models like the Generalized Lotka-Volterra (GLV) framework. In this work, we introduce a hybrid modeling approach that integrates mechanistic insights with machine learning via Physics-Informed Neural Networks (PINNs). By embedding the GLV equations as soft constraints in the neural network's loss function, our method fuses prior biological knowledge with observational data to enable more robust and interpretable parameter inference. This formulation leverages automatic differentiation to enforce consistency with known dynamics while flexibly accommodating noise, missing values, and irregular sampling. We show that this combination of data-driven learning and mechanistic structure improves the identifiability of key parameters - such as species interaction coefficients and intrinsic growth rates - critical for characterizing microbial behavior and enabling cross-condition comparisons. The resulting PINN model also acts as a differentiable and scalable surrogate, suitable for integration into broader frameworks like digital twins. This work contributes to the broader goal of bridging mechanistic modeling and data-driven inference in biomedicine, illustrating how hybrid approaches can enhance the reliability, interpretability, and generalizability of models for complex biological systems.

Please register for the free workshop using the registration button.