arXiv subjects

Reinhard C. Laubenbacher

Publications and source records attributed to Reinhard C. Laubenbacher.

7 recordsLinked to original sources

arXiv2026

Learning dynamical systems with biochemically informed neural ordinary differential equations

Ordinary differential equation models of biochemical reactions are often formulated as stoichiometric systems in which the dynamics arise from a collection of interacting processes. A central challenge is that the functional form of each process is rarely known a priori and may be difficult to infer from data. We propose biochemically informed neural ordinary differential equations (BINODEs), a neural-ODE framework that retains the stoichiometric structure of mechanistic models while representing individual processes by neural networks. In BINODEs, the outputs of neural network processes (NNPs) are mapped to state derivatives through a linear layer analogous to a stoichiometric matrix. This architecture allows biological side information, such as process-specific inputs, sign constraints, and monotonicity assumptions, to be built directly into the model. We characterize the approximation properties of NNPs for several standard biochemical rate laws and show that the proposed framework recovers both trajectories and process-level structure in Monod, Lotka--Volterra, pharmacokinetic, and ultradian endocrine models. These results suggest that BINODEs offer a useful compromise between mechanistic interpretability and data-driven flexibility for modeling partially known biochemical or biological dynamical systems.

math.DS↗

arXiv2025

EFECT: A Method to Quantify the Reproducibility of Stochastic Simulations

Reproducibility is a fundamental requirement for validating scientific claims in computational research. Stochastic computational models are widely used in fields such as systems biology, financial modeling and environmental sciences. However, achieving reproducibility in stochastic simulations remains challenging, as each run can produce different outcomes. Existing infrastructure and software tools do not address independent reproduction of simulation results. Without independent reproducibility, results and conclusions lack credibility, as it remains unclear whether observed findings reflect model behavior or are artifacts of stochastic variation or an underpowered study. To bridge this gap, we introduce the Empirical Characteristic Function Equality Convergence Test (EFECT), a data-driven method to quantify the reproducibility of stochastic simulation results. EFECT employs empirical characteristic functions to compare reported results with those independently generated by assessing distributional inequality, termed EFECT error. Additionally, we establish the EFECT convergence point, a quantitative metric for determining the required number of simulation runs to achieve an EFECT error value of a priori significance. EFECT is applicable to all bounded, real-valued outputs, regardless of the model type or simulation method that produced them. We tested EFECT with over 40 use cases to demonstrate its broad applicability and effectiveness. EFECT standardizes stochastic simulation reproducibility, establishing a workflow that guarantees reliable results, supporting a wide range of stakeholders, and thereby enhancing validation of stochastic simulation studies, across a model's lifecycle. To promote standardization, we are developing the open-source software library libSSR in multiple programming languages for easy integration of EFECT.

stat.ME↗

arXiv2024

Surrogate Modeling and Control of Medical Digital Twins

The vision of personalized medicine is to identify interventions that maintain or restore a person's health based on their individual biology. Medical digital twins, computational models that integrate a wide range of health-related data about a person and can be dynamically updated, are a key technology that can help guide medical decisions. Such medical digital twin models can be high-dimensional, multi-scale, and stochastic. To be practical for healthcare applications, they often need to be simplified into low-dimensional surrogate models that can be used for the optimal design of interventions. This paper introduces surrogate modeling algorithms for the purpose of optimal control applications. As a use case, we focus on agent-based models (ABMs), a common model type in biomedicine for which there are no readily available optimal control algorithms. By deriving surrogate models that are based on systems of ordinary differential equations, we show how optimal control methods can be employed to compute effective interventions, which can then be lifted back to a given ABM. The relevance of the methods introduced here extends beyond medical digital twins to other complex dynamical systems.

q-bio.QM↗

arXiv2024

Control of Medical Digital Twins with Artificial Neural Networks

The objective of personalized medicine is to tailor interventions to an individual patient's unique characteristics. A key technology for this purpose involves medical digital twins, computational models of human biology that can be personalized and dynamically updated to incorporate patient-specific data collected over time. Certain aspects of human biology, such as the immune system, are not easily captured with physics-based models, such as differential equations. Instead, they are often multi-scale, stochastic, and hybrid. This poses a challenge to existing model-based control and optimization approaches that cannot be readily applied to such models. Recent advances in automatic differentiation and neural-network control methods hold promise in addressing complex control problems. However, the application of these approaches to biomedical systems is still in its early stages. This work introduces dynamics-informed neural-network controllers as an alternative approach to control of medical digital twins. As a first use case for this method, the focus is on agent-based models, a versatile and increasingly common modeling platform in biomedicine. The effectiveness of the proposed neural-network control method is illustrated and benchmarked against other methods with two widely-used agent-based model types. The relevance of the method introduced here extends beyond medical digital twins to other complex dynamical systems.

q-bio.QM↗

arXiv2023

Homogeneous Functions and Algebraic $K$--theory

In this paper we develop the theory of homogeneous functions between finite abelian groups. Here, a function $f:G\longrightarrow H$ between finite abelian groups is homogeneous of degree $d$ if $f(nx)=n^df(x)$ for all $x\in G$ and all $n$ which are relatively prime to the order of $x$. We show that the group of homogeneous functions of degree one from a group $G$ of odd order to $\mathbb{Q}/\mathbb{Z}$ maps onto $SK_1(\mathbb{Z}[G])$, generalizing a result of R. Oliver for $p$-groups.

math.KT↗

arXiv2008

Stabilizing and Destabilizing Effects of Embedding 3-node Subgraphs on State Space of Boolean Networks

We demonstrate the effects of embedding subgraphs using a Boolean network, which is one of the discrete dynamical models for transcriptional regulatory networks. After comparing the dynamical properties of network embedded seven different subgraphs including feedback and feedforward subgraphs, we found that complexity of the state space that increases with longer length of attractors and greater number of attractors is reduced for networks with more feedforward subgraphs. In addition, feedforward subgraphs can also provide higher mutual information with lower entropy in a temporal program of gene expression. Networks with other six subgraphs show opposite effects on dynamics of the networks, is roughly consistent with Thomas's conjecture. These results suggest that feedforward subgraphs are one of the favorable local structures in biological complex networks.

nlin.CG↗

arXiv2005

Discretization of Time Series Data

Data discretization, also known as binning, is a frequently used technique in computer science, statistics, and their applications to biological data analysis. We present a new method for the discretization of real-valued data into a finite number of discrete values. Novel aspects of the method are the incorporation of an information-theoretic criterion and a criterion to determine the optimal number of values. While the method can be used for data clustering, the motivation for its development is the need for a discretization algorithm for several multivariate time series of heterogeneous data, such as transcript, protein, and metabolite concentration measurements. As several modeling methods for biochemical networks employ discrete variable states, the method needs to preserve correlations between variables as well as the dynamic features of the time series. A C++ implementation of the algorithm is available from the authors at http://polymath.vbi.vt.edu/discretization .

q-bio.OT↗