Biomedical Mathematics Group

Global Linearization of Nonlinear Dynamics via Koopman Operators: A Gentle Introduction, Applications, and Open Challenges - Hyukpyo Hong
2026-07-28 16:00 - 17:00 (Asia/Seoul) | 108, Conference Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Korea, Republic of
Abstract:
A central challenge of modern dynamical systems theory is to make nonlinear systems tractable without sacrificing fidelity. Koopman operator theory pursues this goal by lifting nonlinear dynamics into a linear, but infinite dimensional, operator acting on a function space. This operator-theoretic perspective underlies a broad class of modern data-driven methods, from dynamic mode decomposition to equation discovery in scientific machine learning for fluid dynamics and neuroscience. Yet this power comes at a price: the operator’s infinite dimensionality poses a fundamental obstacle to computation and practical use, and finding tractable finite-dimensional approximations remains an open and active challenge. In this talk, I will first introduce the basic principles of Koopman operator theory and survey some of the results that have made it a cornerstone of modern dynamical systems analysis. I will then briefly describe two of my works on finite-dimensional Koopman representations. Finally, I will turn to my recent work on non-autonomous dynamical system learning, in collaboration with Prof. Dae Wook Kim.

Fast training of accurate physics-informed neural networks without gradient descent - Seunghun Lee
2026-07-31 10:00 - 12:00 | 108, Conference Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Korea, Republic of
In this talk, we discuss the paper “Fast training of accurate physics-informed neural networks without gradient descent” by Chinmay Datar et al., ICLR, 2026.
Abstract:
Solving time-dependent Partial Differential Equations (PDEs) is one of the most critical problems in computational science. While Physics-Informed Neural Networks (PINNs) offer a promising framework for approximating PDE solutions, their accuracy and training speed are limited by two core barriers: gradient-descent-based iterative optimization over complex loss landscapes and non-causal treatment of time as an extra spatial dimension. We present Frozen-PINN, a novel PINN based on the principle of space-time separation that leverages random features instead of training with gradient descent, and incorporates temporal causality by construction. On nine PDE benchmarks, including challenges like extreme advection speeds, shocks, and high-dimensionality, Frozen-PINNs achieve superior training efficiency and accuracy over state-of-the-art PINNs, often by several orders of magnitude. Our work addresses longstanding training and accuracy bottlenecks of PINNs, delivering quickly trainable, highly accurate, and inherently causal PDE solvers, a combination that prior methods could not realize. Our approach challenges the reliance of PINNs on stochastic gradient-descent-based methods and specialized hardware, leading to a paradigm shift in PINN training and providing a challenging benchmark for the community.

Infection dynamics at the host and cellular levels - Seong Jun Park
2026-08-03 11:00 - 12:00 | B232 Seminar Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Daejeon, 34126, Korea, Republic of
Abstract:
In general, the rates of infection and removal (whether through recovery or death) are nonlinear functions of the number of infected and susceptible individuals. One of the simplest models for the spread of infectious diseases is the SIR model, which categorizes individuals as susceptible, infectious, recovered or deceased. In this model, the infection rate, governing the transition from susceptible to infected individuals, is given by a linear function of both susceptible and infected populations. Similarly, the removal rate, representing the transition from infected to removed individuals, is a linear function of the number of infected individuals. However, existing research often overlooks the impact of nonlinear infection and removal rates in infection dynamics. This work presents an analytic expression for the number of infected individuals considering nonlinear infection and removal rates. In particular, we examine how the number of infected individuals varies as cases emerge and obtain the expression accounting for the number of infected individuals at each moment. Viruses are microscopic infectious agents that require a host cell for replication. Viral replication occurs in several stages, and the completion time for each stage varies due to differences in the cellular environment. Thus, the time to complete each stage in viral replication is a random variable. However, no analytic expression exists for the viral population at the cellular level when the completion time for each process constituting viral replication is a random variable. This study presents a simplified model of viral replication, treating each stage as a renewal process with independently and identically distributed completion times. Using the proposed model, we derive an analytical formula for viral populations at the cellular level, based on viewing viral replication as a birth-death process. The mean viral count is expressed via probability density functions representing the completion time for each step in the replication process. This work validates the results with stochastic simulations. This study provides a new quantitative framework for understanding viral infection dynamics at host and cellular levels.

AutoML-Agent: A Multi-Agent LLM Framework for Full-Pipeline AutoML - Jin Woo Hyun
2026-08-07 10:00 - 12:00 | B232 Seminar Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Daejeon, 34126, Korea, Republic of
In this talk, we discuss the paper “AutoML-Agent: A Multi-Agent LLM Framework for Full-Pipeline AutoML” by Patara Trirat et al, ICML, 2025.
Abstract:
Automated machine learning (AutoML) accelerates AI development by automating tasks in the development pipeline, such as optimal model search and hyperparameter tuning. Existing AutoML systems often require technical expertise to set up complex tools, which is in general time-consuming and requires a large amount of human effort. Therefore, recent works have started exploiting large language models (LLM) to lessen such burden and increase the usability of AutoML frameworks via a natural language interface, allowing non-expert users to build their data-driven solutions. These methods, however, are usually designed only for a particular process in the AI development pipeline and do not efficiently use the inherent capacity of the LLMs. This paper proposes AutoML-Agent, a novel multi-agent framework tailored for full-pipeline AutoML, i.e., from data retrieval to model deployment. AutoML-Agent takes user’s task descriptions, facilitates collaboration between specialized LLM agents, and delivers deployment-ready models. Unlike existing work, instead of devising a single plan, we introduce a retrieval-augmented planning strategy to enhance exploration to search for more optimal plans. We also decompose each plan into sub-tasks (e.g., data preprocessing and neural network design) each of which is solved by a specialized agent we build via prompting executing in parallel, making the search process more efficient. Moreover, we propose a multi-stage verification to verify executed results and guide the code generation LLM in implementing successful solutions. Extensive experiments on seven downstream tasks using fourteen datasets show that AutoML-Agent achieves a higher success rate in automating the full AutoML process, yielding systems with good performance throughout the diverse domains.

Evolution of error correction through a need for speed - Kangmin Lee
2026-08-14 10:00 - 12:00 | 108, Conference Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Korea, Republic of
In this talk, we discuss the paper “Evolution of error correction through a need for speed” by Riccardo Ravasio et al., Science, 2026.
Abstract:
Kinetic proofreading is a class of error-correcting mechanisms in biology that expend energy to avoid mistakes during replication, transcription, and translation. Proofreading is typically assumed to evolve when selection for fidelity outweighs costs in energy and the speed of replication. We show that when stalling after misincorporations is accounted for, proofreading can instead speed up replication. Consistent with data on polymerase mutagenesis, our results suggest that proofreading can evolve under selection for speed alone. We generalize to multicomponent self-assembly and show that analogous error-correcting processes, such as dynamic instability, can likewise emerge purely from selection for rapid assembly. Thus, nonequilibrium error correction can evolve from selection for speed, even without direct fidelity advantages. We discuss implications for mutation-rate evolution, molecular assembly processes, and models of early life.

수학이 공학의 언어라면 - 민태기
2026-08-17 16:00 - 17:00 | 109, Conference room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Korea, Republic of
이번 세미나에서는 “조선이 만난 아인슈타인”, “판타 레이” 등을 저술하신 민태기 소장님을 모시고 “수학이 공학의 언어라면”이라는 주제로 강연을 진행할 예정입니다.

Tangent-Space Regularization for Neural-Network Models of Dynamical Systems - Olive Cawiding
2026-08-21 10:00 - 12:00 | 108, Conference Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Korea, Republic of
In this talk, we discuss the paper “Tangent-Space Regularization for Neural-Network Models of Dynamical Systems” by Fredrik B Carlson et al, arXiv (2026).
Abstract:
This work introduces the concept of tangent space regularization for neural-network models of dynamical systems. The tangent space to the dynamics function of many physical systems of interest in control applications exhibits useful properties, e.g., smoothness, motivating regularization of the model Jacobian along system trajectories using assumptions on the tangent space of the dynamics. Without assumptions, large amounts of training data are required for a neural network to learn the full non-linear dynamics without overfitting. We compare different network architectures on one-step prediction and simulation performance and investigate the propensity of different architectures to learn models with correct input-output Jacobian. Furthermore, the influence of L2 weight regularization on the learned Jacobian eigenvalue spectrum, and hence system stability, is investigated.

Towards a General Intelligence and Interface for Wearable Health Data - Aqsa Awan
2026-08-28 10:00 - 12:00 | 108, Conference Room, IBS, 55 Expo-ro Yuseong-gu, Daejeon, Korea, Republic of
In this talk, we discuss the paper “Towards a General Intelligence and Interface for Wearable Health Data” by Girish Narayanswamy et al., arXiv, 2026.
Abstract:
While ubiquitous wearable sensors capture a wealth of behavioral and physiological information, effectively transforming these signals into personalized health insights is challenging. Specifically, converting low-level sensor data into representations capable of characterizing higher-level states is difficult due to high phenotypic diversity and variation in individual baseline health, physiology, and lifestyle factors. Moreover, collecting wearable data paired with health outcome annotations is laborious and expensive, and retrospective annotation remains practically unfeasible, contributing to a scarcity of data with high-quality labels. To overcome these limitations, we propose a foundation model for wearable health that is pretrained on more than one trillion minutes of unlabeled sensor signals drawn from a large cohort of five million participants. We demonstrate that the joint scaling of model capacity and pretraining data volume leads to systematic improvements in performance, as evaluated on a diverse set of 35 health prediction tasks, spanning cardiovascular, metabolic, sleep, and mental health, as well as lifestyle choices and demographic factors. We find that this population scale representation unlocks label-efficient few-shot learning and generative capabilities for robust daily metric estimation. To further leverage this learned representation, we deploy a classroom of LLM agents to autonomously search the space of downstream predictive heads built on the model embeddings, showing broad performance improvements that increase with LLM model capacity. Finally, we show how integrating these downstream predictors into a Personal Health Agent can support model responses that are more relevant, contextually aware, and safe, and we validate this via 1,860 ratings from a cohort of clinicians.
