arXiv subjects

Jacobo Ayensa-Jiménez

Publications and source records attributed to Jacobo Ayensa-Jiménez.

6 recordsLinked to original sources

arXiv2026

Rate-Independent Epigenetics: a thermodynamically consistent framework for modelling epigenetic response

Epigenetic changes -- heritable, long-lived, yet actively reversible modifications of the chromatin state -- display memory, threshold activation and hysteresis, features that are the hallmark of rate-independent dissipative evolution. We propose a mathematical framework, Rate-Independent Epigenetics, that models epigenetic change within the theory of rate-independent systems and is consistent with two fundamental principles identified with the laws of thermodynamics. In this framework, a model is specified by a state space of epigenetic configurations, a stored-energy functional depending on the state and on an external loading, and a 1-homogeneous dissipation potential encoding the resistance of the epigenetic machinery to change. Assuming an energetic evolution principle, the governing equations follow, with no further modelling hypotheses. The energy balance is exact energy conservation, and the 1-homogeneity of the dissipation potential forces a non-negative, minimal (economical) dissipation. Under natural coercivity and continuity assumptions we establish existence of energetic solutions and, via vanishing viscosity, of balanced-viscosity solutions that resolve the ambiguity of the energetic formulation at epigenetic switches; uniqueness holds under convexity and, in the scalar case, under a mild finite-multiplicity condition. We then build a variational time integrator, prove its convergence to energetic solutions and a global energy-consistency estimate. The framework is illustrated on the scalar linear play operator, on an example with a double-well energetic potential, showing the ability of the framework to study multi-stability scenarios and catastrophic switches and on a nonlinear problem, proving that the theoretical results hold. The presented framework can be seen as a skeleton for a richer thermodynamically-consistent theory incorporating viscous dissipation features.

physics.bio-ph↗

arXiv2025

Enhancing material behavior discovery using embedding-oriented Physically-Guided Neural Networks with Internal Variables

Physically Guided Neural Networks with Internal Variables are SciML tools that use only observable data for training and and have the capacity to unravel internal state relations. They incorporate physical knowledge both by prescribing the model architecture and using loss regularization, thus endowing certain specific neurons with a physical meaning as internal state variables. Despite their potential, these models face challenges in scalability when applied to high-dimensional data such as fine-grid spatial fields or time-evolving systems. In this work, we propose some enhancements to the PGNNIV framework that address these scalability limitations through reduced-order modeling techniques. Specifically, we introduce alternatives to the original decoder structure using spectral decomposition, POD, and pretrained autoencoder-based mappings. These surrogate decoders offer varying trade-offs between computational efficiency, accuracy, noise tolerance, and generalization, while improving drastically the scalability. Additionally, we integrate model reuse via transfer learning and fine-tuning strategies to exploit previously acquired knowledge, supporting efficient adaptation to novel materials or configurations, and significantly reducing training time while maintaining or improving model performance. To illustrate these various techniques, we use a representative case governed by the nonlinear diffusion equation, using only observable data. Results demonstrate that the enhanced PGNNIV framework successfully identifies the underlying constitutive state equations while maintaining high predictive accuracy. It also improves robustness to noise, mitigates overfitting, and reduces computational demands. The proposed techniques can be tailored to various scenarios depending on data availability, resources, and specific modeling objectives, overcoming scalability challenges in all the scenarios.

cs.LG↗

arXiv2023

Predicting and explaining nonlinear material response using deep Physically Guided Neural Networks with Internal Variables

Nonlinear materials are often difficult to model with classical state model theory because they have a complex and sometimes inaccurate physical and mathematical description or we simply do not know how to describe such materials in terms of relations between external and internal variables. In many disciplines, Neural Network methods have arisen as powerful tools to identify very complex and non-linear correlations. In this work, we use the very recently developed concept of Physically Guided Neural Networks with Internal Variables (PGNNIV) to discover constitutive laws using a model-free approach and training solely with measured force-displacement data. PGNNIVs make a particular use of the physics of the problem to enforce constraints on specific hidden layers and are able to make predictions without internal variable data. We demonstrate that PGNNIVs are capable of predicting both internal and external variables under unseen load scenarios, regardless of the nature of the material considered (linear, with hardening or softening behavior and hyperelastic), unravelling the constitutive law of the material hence explaining its nature altogether, placing the method in what is known as eXplainable Artificial Intelligence (XAI).

cs.LG↗

arXiv2022

Cell dynamics in microfluidic devices under heterogeneous chemotaxis and growth conditions: a mathematical study

As motivated by studies of cellular motility driven by spatiotemporal chemotactic gradients in microdevices, we develop a framework for constructing approximate analytical solutions for the location, speed and cellular densities for cell chemotaxis waves in heterogeneous fields of chemoattractant from the underlying partial differential equation models. In particular, such chemotactic waves are not in general translationally invariant travelling waves, but possess a spatial variation that evolves in time, and may even may oscillate back and forth in time, according to the details of the chemotactic gradients. The analytical framework exploits the observation that unbiased cellular diffusive flux is typically small compared to chemotactic fluxes and is first developed and validated for a range of exemplar scenarios. The framework is subsequently applied to more complex models considering the full dynamics of the chemoattractant and how this may be driven and controlled within a microdevice by considering a range of boundary conditions. In particular, even though solutions cannot be constructed in all cases, a wide variety of scenarios can be considered analytically, firstly providing global insight into the important mechanisms and features of cell motility in complex spatiotemporal fields of chemoattractant. Such analytical solutions also provide a means of rapid evaluation of model predictions, with the prospect of application in computationally demanding investigations relating theoretical models and experimental observation, such as Bayesian parameter estimation.

math.AP↗

arXiv2020

On the application of Physically-Guided Neural Networks with Internal Variables to Continuum Problems

Predictive Physics has been historically based upon the development of mathematical models that describe the evolution of a system under certain external stimuli and constraints. The structure of such mathematical models relies on a set of hysical hypotheses that are assumed to be fulfilled by the system within a certain range of environmental conditions. A new perspective is now raising that uses physical knowledge to inform the data prediction capability of artificial neural networks. A particular extension of this data-driven approach is Physically-Guided Neural Networks with Internal Variables (PGNNIV): universal physical laws are used as constraints in the neural network, in such a way that some neuron values can be interpreted as internal state variables of the system. This endows the network with unraveling capacity, as well as better predictive properties such as faster convergence, fewer data needs and additional noise filtering. Besides, only observable data are used to train the network, and the internal state equations may be extracted as a result of the training processes, so there is no need to make explicit the particular structure of the internal state model. We extend this new methodology to continuum physical problems, showing again its predictive and explanatory capacities when only using measurable values in the training set. We show that the mathematical operators developed for image analysis in deep learning approaches can be used and extended to consider standard functional operators in continuum Physics, thus establishing a common framework for both. The methodology presented demonstrates its ability to discover the internal constitutive state equation for some problems, including heterogeneous and nonlinear features, while maintaining its predictive ability for the whole dataset coverage, with the cost of a single evaluation.

cs.LG↗

arXiv2020

Identification of state functions by physically-guided neural networks with physically-meaningful internal layers

Substitution of well-grounded theoretical models by data-driven predictions is not as simple in engineering and sciences as it is in social and economic fields. Scientific problems suffer most times from paucity of data, while they may involve a large number of variables and parameters that interact in complex and non-stationary ways, obeying certain physical laws. Moreover, a physically-based model is not only useful for making predictions, but to gain knowledge by the interpretation of its structure, parameters, and mathematical properties. The solution to these shortcomings seems to be the seamless blending of the tremendous predictive power of the data-driven approach with the scientific consistency and interpretability of physically-based models. We use here the concept of physically-constrained neural networks (PCNN) to predict the input-output relation in a physical system, while, at the same time fulfilling the physical constraints. With this goal, the internal hidden state variables of the system are associated with a set of internal neuron layers, whose values are constrained by known physical relations, as well as any additional knowledge on the system. Furthermore, when having enough data, it is possible to infer knowledge about the internal structure of the system and, if parameterized, to predict the state parameters for a particular input-output relation. We show that this approach, besides getting physically-based predictions, accelerates the training process, reduces the amount of data required to get similar accuracy, filters partly the intrinsic noise in the experimental data and provides improved extrapolation capacity.

cs.LG↗