Paper List
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EnzyCLIP: A Cross-Attention Dual Encoder Framework with Contrastive Learning for Predicting Enzyme Kinetic Constants
This paper addresses the core challenge of jointly predicting enzyme kinetic parameters (Kcat and Km) by modeling dynamic enzyme-substrate interaction...
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Tissue stress measurements with Bayesian Inversion Stress Microscopy
This paper addresses the core challenge of measuring absolute, tissue-scale mechanical stress without making assumptions about tissue rheology, which ...
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DeepFRI Demystified: Interpretability vs. Accuracy in AI Protein Function Prediction
This study addresses the critical gap between high predictive accuracy and biological interpretability in DeepFRI, revealing that the model often prio...
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Hierarchical Molecular Language Models (HMLMs)
This paper addresses the core challenge of accurately modeling context-dependent signaling, pathway cross-talk, and temporal dynamics across multiple ...
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Stability analysis of action potential generation using Markov models of voltage‑gated sodium channel isoforms
This work addresses the challenge of systematically characterizing how the high-dimensional parameter space of Markov models for different sodium chan...
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Personalized optimization of pediatric HD-tDCS for dose consistency and target engagement
This paper addresses the critical limitation of one-size-fits-all HD-tDCS protocols in pediatric populations by developing a personalized optimization...
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Consistent Synthetic Sequences Unlock Structural Diversity in Fully Atomistic De Novo Protein Design
This paper addresses the core pain point of low sequence-structure alignment in existing synthetic datasets (e.g., AFDB), which severely limits the pe...
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Generative design and validation of therapeutic peptides for glioblastoma based on a potential target ATP5A
This paper addresses the critical bottleneck in therapeutic peptide design: how to efficiently optimize lead peptides with geometric constraints while...
Beyond Bayesian Inference: The Correlation Integral Likelihood Framework and Gradient Flow Methods for Deterministic Sampling
Institute of Mathematics, Polish Academy of Sciences | Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw | Institute for Mathematics, Heidelberg University
The 30-Second View
IN SHORT: This paper addresses the core challenge of calibrating complex biological models (e.g., PDEs, agent-based models) with incomplete, noisy, or heterogeneous data, where traditional pointwise comparison methods fail due to system sensitivity and intrinsic variability.
Innovation (TL;DR)
- Methodology Introduces the Correlation Integral Likelihood (CIL) framework, a unified approach for parameter estimation in systems with heterogeneous or chaotic dynamics (e.g., pattern formation, individual-based models), moving beyond classical Bayesian methods.
- Methodology Proposes integration of deterministic gradient flow methods within the CIL framework to enhance inference efficiency and accuracy, compared to traditional stochastic sampling (e.g., MCMC).
- Theory Generalizes the concept of correlation dimension from chaos theory to construct a robust metric for comparing the global geometric structure of model outputs (e.g., attractors, spatial patterns) rather than relying on unstable pointwise comparisons.
Key conclusions
- The CIL method provides a theoretically grounded framework for parameter estimation in systems where solution heterogeneity (e.g., in Turing patterns or chaotic attractors) makes conventional likelihoods ineffective.
- Integrating deterministic gradient flow sampling with the CIL framework can potentially enhance computational efficiency and inference accuracy compared to purely stochastic methods like MCMC, especially for high-dimensional parameter spaces.
- The approach enables reliable model calibration and validation even with incomplete, noisy, or single-snapshot data, advancing the predictive capability and mechanistic understanding of complex biological systems.
Abstract: Calibrating mathematical models of biological processes is essential for achieving predictive accuracy and gaining mechanistic insight. However, this task remains challenging due to limited and noisy data, significant biological variability, and the computational complexity of the models themselves. In this method's article, we explore a range of approaches for parameter inference in partial differential equation (PDE) models of biological systems. We introduce a unified mathematical framework, the Correlation Integral Likelihood (CIL) method, for parameter estimation in systems exhibiting heterogeneous or chaotic dynamics, encompassing both pattern formation models and individual-based models. Departing from classical Bayesian inverse problem methodologies, we motivate the development of the CIL method, demonstrate its versatility, and highlight illustrative applications within mathematical biology. Furthermore, we compare stochastic sampling strategies, such as Markov Chain Monte Carlo (MCMC), with deterministic gradient flow approaches, highlighting how these methods can be integrated within the proposed framework to enhance inference performance. Our work provides a practical and theoretically grounded toolbox for researchers seeking to calibrate complex biological models using incomplete, noisy, or heterogeneous data, thereby advancing both the predictive capability and mechanistic understanding of such systems.