iPINNs: Incremental learning for Physics-informed neural networks

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and non-unique due to the complexity of the loss landscape that needs to be traversed. Although a variety of multi-task learning and transfer learning approaches have been proposed to overcome these issues, there is no incremental training procedure for PINNs that can effectively mitigate such training challenges. We propose incremental PINNs (iPINNs) that can learn multiple tasks (equations) sequentially without additional parameters for new tasks and improve performance for every equation in the sequence. Our approach learns multiple PDEs starting from the simplest one by creating its own subnetwork for each PDE and allowing each subnetwork to overlap with previously learned subnetworks. We demonstrate that previous subnetworks are a good initialization for a new equation if PDEs share similarities. We also show that iPINNs achieve lower prediction error than regular PINNs for two different scenarios: (1) learning a family of equations (e.g., 1-D convection PDE); and (2) learning PDEs resulting from a combination of processes (e.g., 1-D reaction-diffusion PDE). The ability to learn all problems with a single network together with learning more complex PDEs with better generalization than regular PINNs will open new avenues in this field

Compositional Analysis of Lignocellulosic Feedstocks. 2. Method Uncertainties

The most common procedures for characterizing the chemical components of lignocellulosic feedstocks use a two-stage sulfuric acid hydrolysis to fractionate biomass for gravimetric and instrumental analyses. The uncertainty (i.e., dispersion of values from repeated measurement) in the primary data is of general interest to those with technical or financial interests in biomass conversion technology. The composition of a homogenized corn stover feedstock (154 replicate samples in 13 batches, by 7 analysts in 2 laboratories) was measured along with a National Institute of Standards and Technology (NIST) reference sugar cane bagasse, as a control, using this laboratory's suite of laboratory analytical procedures (LAPs). The uncertainty was evaluated by the statistical analysis of these data and is reported as the standard deviation of each component measurement. Censored and uncensored versions of these data sets are reported, as evidence was found for intermittent instrumental and equipment problems. The censored data are believed to represent the “best case” results of these analyses, whereas the uncensored data show how small method changes can strongly affect the uncertainties of these empirical methods. Relative standard deviations (RSD) of 1−3% are reported for glucan, xylan, lignin, extractives, and total component closure with the other minor components showing 4−10% RSD. The standard deviations seen with the corn stover and NIST bagasse materials were similar, which suggests that the uncertainties reported here are due more to the analytical method used than to the specific feedstock type being analyzed

Combined inactivation of the Clostridium cellulolyticum lactate and malate dehydrogenase genes substantially increases ethanol yield from cellulose and switchgrass fermentations

<p>Abstract</p> <p>Background</p> <p>The model bacterium <it>Clostridium cellulolyticum </it>efficiently degrades crystalline cellulose and hemicellulose, using cellulosomes to degrade lignocellulosic biomass. Although it imports and ferments both pentose and hexose sugars to produce a mixture of ethanol, acetate, lactate, H₂and CO₂, the proportion of ethanol is low, which impedes its use in consolidated bioprocessing for biofuels production. Therefore genetic engineering will likely be required to improve the ethanol yield. Plasmid transformation, random mutagenesis and heterologous expression systems have previously been developed for <it>C. cellulolyticum</it>, but targeted mutagenesis has not been reported for this organism, hindering genetic engineering.</p> <p>Results</p> <p>The first targeted gene inactivation system was developed for <it>C. cellulolyticum</it>, based on a mobile group II intron originating from the <it>Lactococcus lactis </it>L1.LtrB intron. This markerless mutagenesis system was used to disrupt both the paralogous <smcaps>L</smcaps>-lactate dehydrogenase (<it>Ccel_2485; ldh</it>) and <smcaps>L</smcaps>-malate dehydrogenase (<it>Ccel_0137; mdh</it>) genes, distinguishing the overlapping substrate specificities of these enzymes. Both mutations were then combined in a single strain, resulting in a substantial shift in fermentation toward ethanol production. This double mutant produced 8.5-times more ethanol than wild-type cells growing on crystalline cellulose. Ethanol constituted 93% of the major fermentation products, corresponding to a molar ratio of ethanol to organic acids of 15, versus 0.18 in wild-type cells. During growth on acid-pretreated switchgrass, the double mutant also produced four times as much ethanol as wild-type cells. Detailed metabolomic analyses identified increased flux through the oxidative branch of the mutant's tricarboxylic acid pathway.</p> <p>Conclusions</p> <p>The efficient intron-based gene inactivation system produced the first non-random, targeted mutations in <it>C. cellulolyticum</it>. As a key component of the genetic toolbox for this bacterium, markerless targeted mutagenesis enables functional genomic research in <it>C</it>. <it>cellulolyticum </it>and rapid genetic engineering to significantly alter the mixture of fermentation products. The initial application of this system successfully engineered a strain with high ethanol productivity from cellobiose, cellulose and switchgrass.</p