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A novel framework is proposed that utilizes symbolic regression via genetic programming to identify free-form partial differential equations from scarce and noisy data. The framework successfully identified ground truth models for four synthetic systems (an isothermal plug flow reactor, a continuously stirred tank reactor, a nonisothermal reactor, and viscous flow governed by Burgers' equation) from time-variant data collected at one location. A comparative analysis against the so-called weak Sparse Identification of Nonlinear Dynamics (SINDy) demonstrated the proposed framework's superior ability to identify meaningful partial differential equation (PDE) models when data was scarce. The framework was further tested for robustness to noise and scarcity, showing successful model recovery from as few as eight time series data points collected at a single point in space with 50% noise. These results emphasize the potential of the proposed framework for the discovery of PDE models when data collection is expensive or otherwise difficult., Competing Interests: Declaration of Generative AI and AI-assisted technologies in the writing process During the preparation of this work the authors used OpenAI’s ChatGPT in order to receive recommended feedback and edits. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of this publication.

Toxic substances, such as polycyclic aromatic hydrocarbons (PAHs) and heavy metals, can accumulate in soil, posing a risk to human health and the environment. To reduce the risk of exposure, rapid identification and remediation of potentially hazardous soils is necessary. Adsorption of contaminants by activated carbons and clay materials is commonly utilized to decrease the bioavailability of chemicals in soil and environmental toxicity in vitro, and this study aims to determine their efficacy in real-life soil samples. Two ecotoxicological models (Lemna minor and Caenorhabditis elegans) were used to test residential soil samples, known to contain an average of 5.3, 262, and 9.6 ppm of PAHs, lead, and mercury, for potential toxicity. Toxicity testing of these soils indicated that 86% and 58% of soils caused ≤50% inhibition of growth and survival of L. minor and C. elegans, respectively. Importantly, 3 soil samples caused ≥90% inhibition of growth in both models, and the toxicity was positively correlated with levels of heavy metals. These toxic soil samples were prioritized for remediation using activated carbon and SM-Tyrosine sorbents, which have been shown to immobilize PAHs and heavy metals, respectively. The inclusion of low levels of SM-Tyrosine protected the growth and survival of L. minor and C. elegans by 83% and 78%, respectively from the polluted soil samples while activated carbon offered no significant protection. These results also indicated that heavy metals were the driver of toxicity in the samples. Results from this study demonstrate that adsorption technologies are effective strategies for remediating complex, real-life soil samples contaminated with hazardous pollutants and protecting natural soil and groundwater resources and habitats. The results highlight the applicability of these ecotoxicological models as rapid screening tools for monitoring soil quality and verifying the efficacy of remediation practices., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

Remediation methods for soil contaminated with poly- and perfluoroalkyl substances (PFAS) are needed to prevent their leaching into drinking water sources and to protect living organisms in the surrounding environment. In this study, the efficacy of processed and amended clays and carbons as soil amendments to sequester PFAS and prevent leaching was assessed using PFAS-contaminated soil and validated using sensitive ecotoxicological bioassays. Four different soil matrices including quartz sand, clay loam soil, garden soil, and compost were spiked with 4 PFAS congeners (PFOA, PFOS, GenX, and PFBS) at 0.01-0.2 μg/mL and subjected to a 3-step extraction method to quantify the leachability of PFAS from each matrix. The multistep extraction method showed that PFAS leaching from soil was aligned with the total carbon content in soil, and the recovery was dependent on concentration of the PFAS. To prevent the leaching of PFAS, several sorbents including activated carbon (AC), calcium montmorillonite (CM), acid processed montmorillonite (APM), and organoclays modified with carnitine, choline, and chlorophyll were added to the four soil matrices at 0.5-4 % w /w, and PFAS was extracted using the LEAF method. Total PFAS bioavailability was reduced by 58-97 % by all sorbents in a dose-dependent manner, with AC being the most efficient sorbent with a reduction of 73-97 %. The water leachates and soil were tested for toxicity using an aquatic plant ( Lemna minor ) and a soil nematode ( Caenorhabditis elegans ), respectively, to validate the reduction in PFAS bioavailability. Growth parameters in both ecotoxicological models showed a dose-dependent reduction in toxicity with value-added growth promotion from the organoclays due to added nutrients. The kinetic studies at varying time intervals and varying pHs simulating acidic rain, fresh water, and brackish water suggested a stable sorption of PFAS on all sorbents that fit the pseudo-second-order for up to 21 days. Contaminated soil with higher than 0.1 μg/mL PFAS may require reapplication of soil amendments every 21 days. Overall, AC showed the highest sorption percentage of total PFAS from in vitro studies, while organoclays delivered higher protection in ecotoxicological models ( in vivo ). This study suggests that in situ immobilization with soil amendments can reduce PFAS leachates and their bioavailability to surrounding organisms. A combination of sorbents may facilitate the most effective remediation of complex soil matrices containing mixtures of PFAS and prevent leaching and uptake into plants., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Pesticides are commonly found in the environment and pose a risk to target and non-target species; therefore, employing a set of bioassays to rapidly assess the toxicity of these chemicals to diverse species is crucial. The toxicity of nine individual pesticides from organophosphate, organochlorine, phenylurea, dinitroaniline, carbamate, and viologen chemical classes and a mixture of all the compounds were tested in three bioassays (Hydra vulgaris, Lemna minor, and Caenorhabditis elegans) that represent plant, aquatic, and soil-dwelling species, respectively. Multiple endpoints related to growth and survival were measured for each model, and EC 10 and EC 50 values were derived for each endpoint to identify sensitivity patterns according to chemical classes and target organisms. L. minor had the lowest EC 10 and EC 50 values for seven and five of the individual pesticides, respectively. L. minor was also one to two orders of magnitude more sensitive to the mixture compared to H. vulgaris and C. elegans, where EC 50 values were calculated to be 0.00042, 0.0014, and 0.038 mM, respectively. H. vulgaris was the most sensitive species to the remaining individual pesticides, and C. elegans consistently ranked the least sensitive to all tested compounds. When comparing the EC 50 values across all pesticides, the endpoints of L. minor were correlated with each other while the endpoints measured in H. vulgaris and C. elegans were clustered together. While there was no apparent relationship between the chemical class of pesticide and toxicity, the compounds were more closely clustered based on target organisms (herbicide vs insecticide). The results of this study demonstrate that the combination of these plant, soil, and aquatic specie can serve as representative indicators of pesticide pollution in environmental samples., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Following the discovery of the least squares method in 1805 by Legendre and later in 1809 by Gauss, surrogate modeling and machine learning have come a long way. From identifying patterns and trends in process data to predictive modeling, optimization, fault detection, reaction network discovery, and process operations, machine learning became an integral part of all aspects of process design and process systems engineering. This is enabled, at the same time necessitated, by the vast amounts of data that are readily available from processes, increased digitalization, automation, increasing computation power, and simulation software that can model complex phenomena that span over several temporal and spatial scales. Although this paper is not a comprehensive review, it gives an overview of the recent history of machine learning models that we use every day and how they shaped process design problems from the recent advances to the exploration of their prospects.