Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of dynamical systems formulates this problem as a linear equation system. Here, we explore several simulation-based optimization approaches, which allow much greater freedom in the objective formulation and weaker conditions on the available data. We show that even for relatively small stochastic population models, simultaneous estimation of parameters and structure poses major challenges for optimization procedures. Particularly, we investigate the application of the local stochastic gradient descent method, commonly used for training machine learning models. We demonstrate accurate estimation of models but find that enforcing the inference of parsimonious, interpretable models drastically increases the difficulty. We give an outlook on how this challenge can be overcome.

Theoretical studies on chemical reaction mechanisms have been crucial in organic chemistry. Traditionally, calculating the manually constructed molecular conformations of transition states for chemical reactions using quantum chemical calculations is the most commonly used method. However, this way is heavily dependent on individual experience and chemical intuition. In our previous study, we proposed a research paradigm that uses enhanced sampling in QM/MM molecular dynamics simulations to study chemical reactions. This approach can directly simulate the entire process of a chemical reaction. However, the computational speed limits the use of high-precision potential energy functions for simulations. To address this issue, we present a scheme for training high-precision force fields for molecular modeling using our developed graph-neural-network-based molecular model, molecular configuration transformer. This potential energy function allows for highly accurate simulations at a low computational cost, leading to more precise calculations of the mechanism of chemical reactions. We have used this approach to study a Cope rearrangement reaction and a Carbonyl insertion reaction catalyzed by Manganese. This "AI+Physics" based simulation approach is expected to become a new trend in the theoretical study of organic chemical reaction mechanisms.

Information processing relying on biochemical interactions in the cellular environment is essential for biological organisms. The implementation of molecular computational systems holds significant interest and potential in the fields of synthetic biology and molecular computation. This two-part article aims to introduce a programmable biochemical reaction network (BCRN) system endowed with mass action kinetics that realizes the fully connected neural network (FCNN) and has the potential to act automatically in vivo. In part I, the feedforward propagation computation, the backpropagation component, and all bridging processes of FCNN are ingeniously designed as specific BCRN modules based on their dynamics. This approach addresses a design gap in the biochemical assignment module and judgment termination module and provides a novel precise and robust realization of bi-molecular reactions for the learning process. Through equilibrium approaching, we demonstrate that the designed BCRN system achieves FCNN functionality with exponential convergence to target computational results, thereby enhancing the theoretical support for such work. Finally, the performance of this construction is further evaluated on two typical logic classification problems.

A combustion chemistry acceleration scheme is developed based on deep operator networks (DeepONets). The scheme is based on the identification of combustion reaction dynamics through a modified DeepOnet architecture such that the solutions of thermochemical scalars are projected to new solutions in small and flexible time increments. The approach is designed to efficiently implement chemistry acceleration without the need for computationally expensive integration of stiff chemistry. An additional framework of latent-space dynamics identification with modified DeepOnet is also proposed which enhances the computational efficiency and widens the applicability of the proposed scheme. The scheme is demonstrated on simple chemical kinetics of hydrogen oxidation to more complex chemical kinetics of n-dodecane high- and low-temperature oxidations. The proposed framework accurately learns the chemical kinetics and efficiently reproduces species and temperature temporal profiles corresponding to each application. In addition, a very large speed-up with a great extrapolation capability is also observed with the proposed scheme.

The inference of chemical reaction networks is an important task in understanding the chemical processes in life sciences and environment. Yet, only a few reaction systems are well-understood due to a large number of important reaction pathways involved but still unknown. Revealing unknown reaction pathways is an important task for scientific discovery that takes decades and requires lots of expert knowledge. This work presents a neural network approach for discovering unknown reaction pathways from concentration time series data. The neural network denoted as Chemical Reaction Neural Network (CRNN), is designed to be equivalent to chemical reaction networks by following the fundamental physics laws of the Law of Mass Action and Arrhenius Law. The CRNN is physically interpretable, and its weights correspond to the reaction pathways and rate constants of the chemical reaction network. Then, inferencing the reaction pathways and the rate constants are accomplished by training the equivalent CRNN via stochastic gradient descent. The approach precludes the need for expert knowledge in proposing candidate reactions, such that the inference is autonomous and applicable to new systems for which there is no existing empirical knowledge to propose reaction pathways. The physical interpretability also makes the CRNN not only capable of fitting the data for a given system but also developing knowledge of unknown pathways that could be generalized to similar chemical systems. Finally, the approach is applied to several chemical systems in chemical engineering and biochemistry to demonstrate its robustness and generality.

With a view towards molecular communication systems and molecular multi-agent systems, we propose the Chemical Baum-Welch Algorithm, a novel reaction network scheme that learns parameters for Hidden Markov Models (HMMs). Each reaction in our scheme changes only one molecule of one species to one molecule of another. The reverse change is also accessible but via a different set of enzymes, in a design reminiscent of futile cycles in biochemical pathways. We show that every fixed point of the Baum-Welch algorithm for HMMs is a fixed point of our reaction network scheme, and every positive fixed point of our scheme is a fixed point of the Baum-Welch algorithm. We prove that the "Expectation" step and the "Maximization" step of our reaction network separately converge exponentially fast. We simulate mass-action kinetics for our network on an example sequence, and show that it learns the same parameters for the HMM as the Baum-Welch algorithm.