Blow-up analysis in a quasilinear parabolic system coupled via nonlinear boundary flux

This paper deals with the blow-up of the solution for a system of evolution pLaplacian equations uit = div(|∇ui p−2∇ui) (i = 1, 2, . . . , k) with nonlinear boundary flux. Under certain conditions on the nonlinearities and data, it is shown that blow-up will occur at some finite time. Moreover, when blow-up does occur, we obtain the upper and lower bounds for the blow-up time. This paper generalizes the previous results

A Narrative Review on Environmental Impacts of Cannabis Cultivation

Interest in growing cannabis for medical and recreational purposes is increasing worldwide. This study reviews the environmental impacts of cannabis cultivation. Results show that both indoor and outdoor cannabis growing is water-intensive. The high water demand leads to water pollution and diversion, which could negatively affect the ecosystem. Studies found out that cannabis plants emit a significant amount of biogenic volatile organic compounds, which could cause indoor air quality issues. Indoor cannabis cultivation is energy-consuming, mainly due to heating, ventilation, air conditioning, and lighting. Energy consumption leads to greenhouse gas emissions. Cannabis cultivation could directly contribute to soil erosion. Meanwhile, cannabis plants have the ability to absorb and store heavy metals. It is envisioned that technologies such as precision irrigation could reduce water use, and application of tools such as life cycle analysis would advance understanding of the environmental impacts of cannabis cultivation

Impedance-based moisture content sensor assessment for gas-phase biofilters

A woodchips-based gas-phase biofilter is capable of mitigating airborne ammonia efficiently. The moisture content (MC) of the biofilter media is important to determine ammonia mitigation and nitrous oxide generation. It is critical to monitor real-time moisture content of the biofilter media for maintaining biofilter performance. The objectives of this research are to obtain a deep insight into the impedance-based moisture content measurement and to improve methodologies to monitor the moisture content of gas-phase biofilters. A sensor consisting of a sensing unit (three parallel plates) and a circuit generating DC voltage outputs was used in this study to measure moisture content. The sensor readings changed with step-wise increase of moisture content as well as different particle size distribution and nitrogen (ammonia-nitrogen, nitrate-nitrogen) concentrations of biofilter media. The results show that both particle size distribution and nitrogen concentrations significantly affected impedance-based moisture sensing. A mathematical model was formulated, which was able to demonstrate the relationship between the sensor reading and moisture content of the biofilter media. A model was established to predict the moisture content of the biofilter media based on sensor reading, ammonia-nitrogen concentration and nitrate-nitrogen concentration

Building Emotional Support Chatbots in the Era of LLMs

The integration of emotional support into various conversational scenarios presents profound societal benefits, such as social interactions, mental health counseling, and customer service. However, there are unsolved challenges that hinder real-world applications in this field, including limited data availability and the absence of well-accepted model training paradigms. This work endeavors to navigate these challenges by harnessing the capabilities of Large Language Models (LLMs). We introduce an innovative methodology that synthesizes human insights with the computational prowess of LLMs to curate an extensive emotional support dialogue dataset. Our approach is initiated with a meticulously designed set of dialogues spanning diverse scenarios as generative seeds. By utilizing the in-context learning potential of ChatGPT, we recursively generate an ExTensible Emotional Support dialogue dataset, named ExTES. Following this, we deploy advanced tuning techniques on the LLaMA model, examining the impact of diverse training strategies, ultimately yielding an LLM meticulously optimized for emotional support interactions. An exhaustive assessment of the resultant model showcases its proficiency in offering emotional support, marking a pivotal step in the realm of emotional support bots and paving the way for subsequent research and implementations

Energy stable and maximum bound principle preserving schemes for the Q-tensor flow of liquid crystals

In this paper, we propose two efficient fully-discrete schemes for Q-tensor flow of liquid crystals by using the first- and second-order stabilized exponential scalar auxiliary variable (sESAV) approach in time and the finite difference method for spatial discretization. The modified discrete energy dissipation laws are unconditionally satisfied for both two constructed schemes. A particular feature is that, for two-dimensional (2D) and a kind of three-dimensional (3D) Q-tensor flows, the unconditional maximum-bound-principle (MBP) preservation of the constructed first-order scheme is successfully established, and the proposed second-order scheme preserves the discrete MBP property with a mild restriction on the time-step sizes. Furthermore, we rigorously derive the corresponding error estimates for the fully-discrete second-order schemes by using the built-in stability results. Finally, various numerical examples validating the theoretical results, such as the orientation of liquid crystal in 2D and 3D, are presented for the constructed schemes

Learned 1-D advection solver to accelerate air quality modeling

Accelerating the numerical integration of partial differential equations by learned surrogate model is a promising area of inquiry in the field of air pollution modeling. Most previous efforts in this field have been made on learned chemical operators though machine-learned fluid dynamics has been a more blooming area in machine learning community. Here we show the first trial on accelerating advection operator in the domain of air quality model using a realistic wind velocity dataset. We designed a convolutional neural network-based solver giving coefficients to integrate the advection equation. We generated a training dataset using a 2nd order Van Leer type scheme with the 10-day east-west components of wind data on 39$^{\circ}$N within North America. The trained model with coarse-graining showed good accuracy overall, but instability occurred in a few cases. Our approach achieved up to 12.5$\times$ acceleration. The learned schemes also showed fair results in generalization tests.Comment: Accepted as a workshop paper at the The Symbiosis of Deep Learning and Differential Equations (DLDE) - II in the 36th Conference on Neural Information Processing Systems (NeurIPS 2022

Learned 1-D passive scalar advection to accelerate chemical transport modeling: a case study with GEOS-FP horizontal wind fields

We developed and applied a machine-learned discretization for one-dimensional (1-D) horizontal passive scalar advection, which is an operator component common to all chemical transport models (CTMs). Our learned advection scheme resembles a second-order accuracy, three-stencil numerical solver, but differs from a traditional solver in that coefficients for each equation term are output by a neural network rather than being theoretically-derived constants. We downsampled higher-resolution simulation results -- resulting in up to 16$\times$ larger grid size and 64$\times$ larger timestep -- and trained our neural network-based scheme to match the downsampled integration data. In this way, we created an operator that is low-resolution (in time or space) but can reproduce the behavior of a high-resolution traditional solver. Our model shows high fidelity in reproducing its training dataset (a single 10-day 1-D simulation) and is similarly accurate in simulations with unseen initial conditions, wind fields, and grid spacing. In many cases, our learned solver is more accurate than a low-resolution version of the reference solver, but the low-resolution reference solver achieves greater computational speedup (500$\times$ acceleration) over the high-resolution simulation than the learned solver is able to (18$\times$ acceleration). Surprisingly, our learned 1-D scheme -- when combined with a splitting technique -- can be used to predict 2-D advection, and is in some cases more stable and accurate than the low-resolution reference solver in 2-D. Overall, our results suggest that learned advection operators may offer a higher-accuracy method for accelerating CTM simulations as compared to simply running a traditional integrator at low resolution

HyperTime: Hyperparameter Optimization for Combating Temporal Distribution Shifts

In this work, we propose a hyperparameter optimization method named \emph{HyperTime} to find hyperparameters robust to potential temporal distribution shifts in the unseen test data. Our work is motivated by an important observation that it is, in many cases, possible to achieve temporally robust predictive performance via hyperparameter optimization. Based on this observation, we leverage the `worst-case-oriented' philosophy from the robust optimization literature to help find such robust hyperparameter configurations. HyperTime imposes a lexicographic priority order on average validation loss and worst-case validation loss over chronological validation sets. We perform a theoretical analysis on the upper bound of the expected test loss, which reveals the unique advantages of our approach. We also demonstrate the strong empirical performance of the proposed method on multiple machine learning tasks with temporal distribution shifts.Comment: 19 pages, 7 figure