The inputs of deep neural network (DNN) from real-world data usually come with uncertainties. Yet, it is challenging to propagate the uncertainty in the input features to the DNN predictions at a low computational cost. This work employs a gradient-based subspace method and response surface technique to accelerate the uncertainty propagation in DNN. Specifically, the active subspace method is employed to identify the most important subspace in the input features using the gradient of the DNN output to the inputs. Then the response surface within that low-dimensional subspace can be efficiently built, and the uncertainty of the prediction can be acquired by evaluating the computationally cheap response surface instead of the DNN models. In addition, the subspace can help explain the adversarial examples. The approach is demonstrated in MNIST datasets with a convolutional neural network. Code is available at: https://github.com/jiweiqi/nnsubspace.
Weiqi Ji, Franz Richter, Michael J. Gollner et al.
Modeling the burning processes of biomass such as wood, grass, and crops is crucial for the modeling and prediction of wildland and urban fire behavior. Despite its importance, the burning of solid fuels remains poorly understood, which can be partly attributed to the unknown chemical kinetics of most solid fuels. Most available kinetic models were built upon expert knowledge, which requires chemical insights and years of experience. This work presents a framework for autonomously discovering biomass pyrolysis kinetic models from thermogravimetric analyzer (TGA) experimental data using the recently developed chemical reaction neural networks (CRNN). The approach incorporated the CRNN model into the framework of neural ordinary differential equations to predict the residual mass in TGA data. In addition to the flexibility of neural-network-based models, the learned CRNN model is interpretable, by incorporating the fundamental physics laws, such as the law of mass action and Arrhenius law, into the neural network structure. The learned CRNN model can then be translated into the classical forms of biomass chemical kinetic models, which facilitates the extraction of chemical insights and the integration of the kinetic model into large-scale fire simulations. We demonstrated the effectiveness of the framework in predicting the pyrolysis and oxidation of cellulose. This successful demonstration opens the possibility of rapid and autonomous chemical kinetic modeling of solid fuels, such as wildfire fuels and industrial polymers.
Data-driven dynamic models of cell biology can be used to predict cell response to unseen perturbations. Recent work (CellBox) had demonstrated the derivation of interpretable models with explicit interaction terms, in which the parameters were optimized using machine learning techniques. While the previous work was tested only in a single biological setting, this work aims to extend the range of applicability of this model inference approach to a diversity of biological systems. Here we adapted CellBox in Julia differential programming and augmented the method with adjoint algorithms, which has recently been used in the context of neural ODEs. We trained the models using simulated data from both abstract and biology-inspired networks, which afford the ability to evaluate the recovery of the ground truth network structure. The resulting accuracy of prediction by these models is high both in terms of low error against data and excellent agreement with the network structure used for the simulated training data. While there is no analogous ground truth for real life biological systems, this work demonstrates the ability to construct and parameterize a considerable diversity of network models with high predictive ability. The expectation is that this kind of procedure can be used on real perturbation-response data to derive models applicable to diverse biological systems.
Chemical reactions occur in energy, environmental, biological, and many other natural systems, and the inference of the reaction networks is essential to understand and design the chemical processes in engineering and life sciences. Yet, revealing the reaction pathways for complex systems and processes is still challenging due to the lack of knowledge of the involved species and reactions. Here, we present a neural network approach that autonomously discovers reaction pathways from the time-resolved species concentration data. The proposed Chemical Reaction Neural Network (CRNN), by design, satisfies the fundamental physics laws, including the Law of Mass Action and the Arrhenius Law. Consequently, the CRNN is physically interpretable such that the reaction pathways can be interpreted, and the kinetic parameters can be quantified simultaneously from the weights of the neural network. The inference of the chemical pathways is accomplished by training the CRNN with species concentration data via stochastic gradient descent. We demonstrate the successful implementations and the robustness of the approach in elucidating the chemical reaction pathways of several chemical engineering and biochemical systems. The autonomous inference by the CRNN approach precludes the need for expert knowledge in proposing candidate networks and addresses the curse of dimensionality in complex systems. The physical interpretability also makes the CRNN capable of not only fitting the data for a given system but also developing knowledge of unknown pathways that could be generalized to similar chemical systems.