Thomas Martini Jørgensen

In biomedical engineering, earthquake prediction, and underground energy harvesting, it is crucial to indirectly estimate the physical properties of porous media since the direct measurement of those are usually impractical/prohibitive. Here we apply the physics-informed neural networks to solve the inverse problem with regard to the nonlinear Biot's equations. Specifically, we consider batch training and explore the effect of different batch sizes. The results show that training with small batch sizes, i.e., a few examples per batch, provides better approximations (lower percentage error) of the physical parameters than using large batches or the full batch. The increased accuracy of the physical parameters, comes at the cost of longer training time. Specifically, we find the size should not be too small since a very small batch size requires a very long training time without a corresponding improvement in estimation accuracy. We find that a batch size of 8 or 32 is a good compromise, which is also robust to additive noise in the data. The learning rate also plays an important role and should be used as a hyperparameter.

This paper presents the potential of applying physics-informed neural networks for solving nonlinear multiphysics problems, which are essential to many fields such as biomedical engineering, earthquake prediction, and underground energy harvesting. Specifically, we investigate how to extend the methodology of physics-informed neural networks to solve both the forward and inverse problems in relation to the nonlinear diffusivity and Biot’s equations. We explore the accuracy of the physics-informed neural networks with different training example sizes and choices of hyperparameters. The impacts of the stochastic variations between various training realizations are also investigated. In the inverse case, we also study the effects of noisy measurements. Furthermore, we address the challenge of selecting the hyperparameters of the inverse model and illustrate how this challenge is linked to the hyperparameters selection performed for the forward one.

This paper presents the potential of applying physics-informed neural networks for solving nonlinear multiphysics problems, which are essential to many fields such as biomedical engineering, earthquake prediction, and underground energy harvesting. Specifically, we investigate how to extend the methodology of physics-informed neural networks to solve both the forward and inverse problems in relation to the nonlinear diffusivity and Biot's equations. We explore the accuracy of the physics-informed neural networks with different training example sizes and choices of hyperparameters. The impacts of the stochastic variations between various training realizations are also investigated. In the inverse case, we also study the effects of noisy measurements. Furthermore, we address the challenge of selecting the hyperparameters of the inverse model and illustrate how this challenge is linked to the hyperparameters selection performed for the forward one.

Safety and efficiency of modern industrial plants can be improved by providing operators with effective digital assistants to diagnose abnormal situations occurring in the plant. To make sense of a large number of alarms, root cause analysis can help pinpoint the origin of an abnormal situation. We investigate the translation of qualitative causal models into Bayesian belief networks (BBN) to utilize efficient tools for probability inference. The diagnosis result of a fault scenario of the Tennessee-Eastman-Process highlight the feasibility of the principle approach and the ongoing research aims to fully leverage the potential of BBN.

Efficient regeneration of NAD(P) ⁺ cofactors is essential for large‐scale application of alcohol dehydrogenases due to the high cost and chemical instability of these cofactors. NAD(P) ⁺ can be regenerated effectively using NAD(P)H oxidases (NOXs) that require molecular oxygen as a cosubstrate. In large‐scale biocatalytic processes, agitation and aeration are needed for sufficient oxygen transfer into the liquid phase, both of which have been shown to significantly increase the rate of enzyme deactivation. As such, the aim of this study was to identify the existence of a correlation between enzyme stability and gas–liquid interfacial area inside the bioreactor. This was done by measuring gas–liquid interfacial areas inside an aerated stirred reactor, using an in situ optical probe, and simultaneously measuring the kinetic stability of NOXs. Following enzyme incubation at various power inputs and gas‐phase compositions, the residual activity was assessed and video samples were analyzed through an image processing algorithm. Enzyme deactivation was found to be proportional to an increase in interfacial area up to a certain limit, where power input appears to have a higher impact. Furthermore, the presence of oxygen increased enzyme deactivation rates at low interfacial areas. The areas were validated with defined glass beads and found to be in the range of those in large‐scale bioreactors. Finally, a correlation between the enzyme half‐life and specific interfacial area was obtained. Therefore, we conclude that the method developed in this contribution can help to predict the behavior of biocatalyst stability under industrially relevant conditions, concerning specific gas–liquid interfacial areas.

Back scatter interferometry (BSI) is a sensitive method for detecting changes in the bulk refractive index of a solution in a microfluidic system. Here we demonstrate that BSI can be used to directly detect enzymatic reactions and, for the first time, derive kinetic parameters. While many methods in biomedical assays rely on detectable biproducts to produce a signal, direct detection is possible if the substrate or the product exert distinct differences in their specific refractive index so that the total refractive index changes during the enzymatic reaction. In this study, both the conversion of glucose to glucose-6-phosphate, catalyzed by hexokinase, and the conversion of adenosine-triphosphate to adenosine di-phosphate and mono-phosphate, catalyzed by apyrase, were monitored by BSI. When adding hexokinase to glucose solutions containing adenosine-triphosphate, the conversion can be directly followed by BSI, which shows the increasing refractive index and a final plateau corresponding to the particular concentration. From the initial reaction velocities, K_M was found to be 0.33 mM using Michaelis–Menten kinetics. The experiments with apyrase indicate that the refractive index also depends on the presence of various ions that must be taken into account when using this technique. This study clearly demonstrates that measuring changes in the refractive index can be used for the direct determination of substrate concentrations and enzyme kinetics.