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The popularity of molecular computation has given rise to several models of abstraction, one of the more recent ones being Chemical Reaction Networks (CRNs). These are equivalent to other popular computational models, such as Vector…
Chemical Reaction Networks (CRNs) are a well-established model of distributed computing characterized by quantities of molecular species that can transform or change through applications of reactions. A fundamental problem in CRNs is the…
Bilinear pooling of Convolutional Neural Network (CNN) features [22, 23], and their compact variants [10], have been shown to be effective at fine-grained recognition, scene categorization, texture recognition, and visual question-answering…
Evolutionary algorithms (EAs) are very popular tools to design and evolve artificial neural networks (ANNs), especially to train them. These methods have advantages over the conventional backpropagation (BP) method because of their low…
Automated mathematical reasoning is a challenging problem that requires an agent to learn algebraic patterns that contain long-range dependencies. Two particular tasks that test this type of reasoning are (1) mathematical equation…
The potential of synthetic biology techniques for designing complex cellular circuits able to solve complicated computations opens a whole domain of exploration, beyond experiments and theory. Such cellular circuits could be used to carry…
Traditional numerical methods, such as the finite element method and finite volume method, adress partial differential equations (PDEs) by discretizing them into algebraic equations and solving these iteratively. However, this process is…
For the investigation of chemical reaction networks, the efficient and accurate determination of all relevant intermediates and elementary reactions is mandatory. The complexity of such a network may grow rapidly, in particular if reactive…
Autocatalysis is an important feature of metabolic networks, contributing crucially to the self-maintenance of organisms. Autocatalytic subsystems of chemical reaction networks (CRNs) are characterized in terms of algebraic conditions on…
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
A family of results, referred to as inheritance results, tell us which enlargements of a chemical reaction network (CRN) preserve its capacity for nontrivial behaviours such as multistationarity and oscillation. In this paper, the following…
Chemical kinetics mechanisms are essential for understanding, analyzing, and simulating complex combustion phenomena. In this study, a Neural Ordinary Differential Equation (Neural ODE) framework is employed to optimize kinetics parameters…
The study of the dynamics of chemical reactions, and in particular phenomena such as oscillating reactions, has led to the recognition that many dynamical properties of a chemical reaction can be predicted from graph theoretical properties…
We propose a direct optimization framework for learning reduced and sparse chemical reaction networks (CRNs) from time-series trajectory data. In contrast to widely used indirect methods-such as those based on sparse identification of…
The theory of computer science is based around Universal Turing Machines (UTMs): abstract machines able to execute all possible algorithms. Modern digital computers are physical embodiments of UTMs. The nondeterministic polynomial (NP) time…
We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the…
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial…
The existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and…
Living systems operate out of equilibrium, continuously consuming energy to sustain organised, functional states. Their emergent behaviour usually relies on a set of interconnected chemical reaction networks (CRNs) driven by external fluxes…
Recent work provides promising evidence that Physics-Informed Neural Networks (PINN) can efficiently solve partial differential equations (PDE). However, previous works have failed to provide guarantees on the worst-case residual error of a…