The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often result in models that lack physical meaning and interpretability, let alone represent the true physics of the system. We propose an unsupervised parameter estimation methodology that first finds an approximate general solution, followed by a spline transformation to linearly estimate the coefficients of the governing ordinary differential equation (ODE). The approximate general solution is postulated using the same functional form as the analytical solution of a general homogeneous, linear, constant-coefficient ODE. An added advantage is its ability to produce a high-fidelity, smooth functional form even in the presence of noisy data. The spline approximation obtains gradient information from the functional form which are linearly independent and creates the basis of the gradient matrix. This gradient matrix is used in a linear system to find the coefficients of the ODEs. From the case studies, we observed that our modeling approach discovers ODEs with high accuracy and also promotes sparsity in the solution without using any regularization techniques. The methodology is also robust to noisy data and thus allows the integration of data-driven techniques into real experimental setting for data-driven learning of physical phenomena.

Tropospheric ozone, known as a concerning air pollutant, has been associated with health issues including asthma, bronchitis, and impaired lung function. The rates at which peroxy radicals react with NO play a critical role in the overall formation and depletion of tropospheric ozone. However, obtaining comprehensive kinetic data for these reactions remains challenging. Traditional approaches to determine rate constants are costly and technically intricate. Fortunately, the emergence of machine learning-based models offers a less resource and time-intensive alternative for acquiring kinetics information. In this study, we leveraged deep reinforcement learning to predict ranges of rate constants (\textit{k}) with exceptional accuracy, achieving a testing set accuracy of 100%. To analyze reactivity trends based on the molecular structure of peroxy radicals, we employed 51 global descriptors as input parameters. These descriptors were derived from optimized minimum energy geometries of peroxy radicals using the quantum composite G3B3 method. Through the application of Integrated Gradients (IGs), we gained valuable insights into the significance of the various descriptors in relation to reaction rates. We successfully validated and contextualized our findings by conducting cross-comparisons with established trends in the existing literature. These results establish a solid foundation for pioneering advancements in chemistry, where computer analysis serves as an inspirational source driving innovation.

We perform a set of flow and reactive transport simulations within three-dimensional fracture networks to learn the factors controlling mineral reactions. CO$_2$ mineralization requires CO$_2$-laden water, dissolution of a mineral that then leads to precipitation of a CO$_2$-bearing mineral. Our discrete fracture networks (DFN) are partially filled with quartz that gradually dissolves until it reaches a quasi-steady state. At the end of the simulation, we measure the quartz remaining in each fracture within the domain. We observe that a small backbone of fracture exists, where the quartz is fully dissolved which leads to increased flow and transport. However, depending on the DFN topology and the rate of dissolution, we observe a large variability of these changes, which indicates an interplay between the fracture network structure and the impact of geochemical dissolution. In this work, we developed a machine learning framework to extract the important features that support mineralization in the form of dissolution. In addition, we use structural and topological features of the fracture network to predict the remaining quartz volume in quasi-steady state conditions. As a first step to characterizing carbon mineralization, we study dissolution with this framework. We studied a variety of reaction and fracture parameters and their impact on the dissolution of quartz in fracture networks. We found that the dissolution reaction rate constant of quartz and the distance to the flowing backbone in the fracture network are the two most important features that control the amount of quartz left in the system. For the first time, we use a combination of a finite-volume reservoir model and graph-based approach to study reactive transport in a complex fracture network to determine the key features that control dissolution.

Can a micron sized sack of interacting molecules autonomously learn an internal model of a complex and fluctuating environment? We draw insights from control theory, machine learning theory, chemical reaction network theory, and statistical physics to develop a general architecture whereby a broad class of chemical systems can autonomously learn complex distributions. Our construction takes the form of a chemical implementation of machine learning's optimization workhorse: gradient descent on the relative entropy cost function. We show how this method can be applied to optimize any detailed balanced chemical reaction network and that the construction is capable of using hidden units to learn complex distributions. This result is then recast as a form of integral feedback control. Finally, due to our use of an explicit physical model of learning, we are able to derive thermodynamic costs and trade-offs associated to this process.

Accurate low dimension chemical kinetic models for methane are an essential component in the design of efficient gas turbine combustors. Kinetic models coupled to computational fluid dynamics (CFD) provide quick and efficient ways to test the effect of operating conditions, fuel composition and combustor design compared to physical experiments. However, detailed chemical kinetic models are too computationally expensive for use in CFD. We propose a novel data orientated three-step methodology to produce compact models that replicate a target set of detailed model properties to a high fidelity. In the first step, a reduced kinetic model is obtained by removing all non-essential species from the detailed model containing 118 species using path flux analysis (PFA). It is then numerically optimised to replicate the detailed model's prediction in two rounds; First, to selected species (OH,H,CO and CH4) profiles in perfectly stirred reactor (PSR) simulations and then re-optimised to the detailed model's prediction of the laminar flame speed. This is implemented by a purposely developed Machine Learned Optimisation of Chemical Kinetics (MLOCK) algorithm. The MLOCK algorithm systematically perturbs all three Arrhenius parameters for selected reactions and assesses the suitability of the new parameters through an objective error function which quantifies the error in the compact model's calculation of the optimisation target. This strategy is demonstrated through the production of a 19 species and a 15 species compact model for methane/air combustion. Both compact models are validated across a range of 0D and 1D calculations across both lean and rich conditions and shows good agreement to the parent detailed mechanism. The 15 species model is shown to outperform the current state-of-art models in both accuracy and range of conditions the model is valid over.

Understanding the set of elementary steps and kinetics in each reaction is extremely valuable to make informed decisions about creating the next generation of catalytic materials. With physical and mechanistic complexity of industrial catalysts, it is critical to obtain kinetic information through experimental methods. As such, this work details a methodology based on the combination of transient rate/concentration dependencies and machine learning to measure the number of active sites, the individual rate constants, and gain insight into the mechanism under a complex set of elementary steps. This new methodology was applied to simulated transient responses to verify its ability to obtain correct estimates of the micro-kinetic coefficients. Furthermore, experimental CO oxidation data was analyzed to reveal the Langmuir-Hinshelwood mechanism driving the reaction. As oxygen accumulated on the catalyst, a transition in the mechanism was clearly defined in the machine learning analysis due to the large amount of kinetic information available from transient reaction techniques. This methodology is proposed as a new data driven approach to characterize how materials control complex reaction mechanisms relying exclusively on experimental data.

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.

Time series models such as dynamical systems are frequently fitted to a cohort of data, ignoring variation between individual entities such as patients. In this paper we show how these models can be personalised to an individual level while retaining statistical power, via use of multi-task learning (MTL). To our knowledge this is a novel development of MTL which applies to time series both with and without control inputs. The modelling framework is demonstrated on a physiological drug response problem which results in improved predictive accuracy and uncertainty estimation over existing state-of-the-art models.