Historical Samples Research Articles

Transferring knowledge by budget online learning for multiobjective multitasking optimization

Multiobjective multitasking optimization (MO-MTO) has attracted increasing attention in the evolutionary computation field. Evolutionary multitasking (EMT) algorithms can improve the overall performance of multiple multiobjective optimization tasks through transferring knowledge among tasks. Negative transfer resulting from the indeterminacy of the transferred knowledge may bring about the degradation of the algorithm performance. Identifying the valuable knowledge to transfer by learning the historical samples is a feasible way to reduce negative transfer. Taking this into account, this paper proposes a budget online learning based EMT algorithm for MO-MTO problems. Specifically, by regarding the historical transferred solutions as samples, a classifier would be trained to identified the valuable knowledge. The solutions which are considered containing valuable knowledge will have more opportunity to be transfer. For the samples arrive in the form of streaming data, the classifier would be updated in a budget online learning way during the evolution process to address the concept drift problem. Furthermore, the exceptional case that the classifier fails to identify the valuable knowledge is considered. Experimental results on two MO-MTO test suits show that the proposed algorithm achieves highly competitive performance compared with several traditional and state-of-the-art EMT methods.

Stable Isotope Analysis of Planktonic Lower Food Webs of Lakes Erie, Huron, Michigan and Superior

Historical plankton samples from the St. Lawrence Great Lakes were subjected to taxon-specific 15N analysis to test the hypothesis that the changes recorded in zooplankton communities during the 21st Century are related to changes in the trophic positions of large-bodied carnivorous copepods. Daphnia mendotae was used as the reference herbivore for trophic-level comparisons. The results were that Limnocalanus macrurus, Diaptomus (Leptodiaptomus) sicilis as well as the cladoceran Bythotrephes cederstroemi show evidence of elevated carnivory compared to data from the 20th Century. The large diaptomid Diaptomus (Leptodiaptomus) sicilis has a stable isotope signature that is significantly more carnivorous in Lake Superior than in Lakes Michigan and Huron by approximately one-half trophic level. Differences were found in 10 cases out of 15 for Limnocalanus (Huron, Michigan Superior), 6 cases out of 15 for Diaptomus (Huron, Michigan) and in 1 out of 1 for Senecella (Superior). We did not find evidence to support the theory that large-bodied calanoid copepods may have improved their representation in the food webs of the upper Great Lakes by shifting their trophic position downward. Instead, large-bodied Calanoida have increased their trophic positions in parallel with their increased relative abundance. More research is thus needed to explain the driving forces for changing food web dynamics in the Great Lakes.

Temporal-Incremental Learning for Android Malware Detection

Malware classification is a specific and refined task within the broader malware detection problem. Effective classification aids in understanding attack techniques and developing robust defenses, ensuring application security and timely mitigation of software vulnerabilities. The dynamic nature of malware demands adaptive classification techniques that can handle the continuous emergence of new families. Traditionally, this is done by retraining models on all historical samples, which requires significant resources in terms of time and storage. An alternative approach is Class-Incremental Learning (CIL), which focuses on progressively learning new classes (malware families) while preserving knowledge from previous training steps. However, CIL assumes that each class appears only once in training and is not revisited, an assumption that does not hold for malware families, which often persist across multiple time intervals. This leads to shifts in the data distribution for the same family over time, a challenge that is not addressed by traditional CIL methods. We formulate this problem as Temporal-Incremental Malware Learning (TIML), which adapts to these shifts and effectively classifies new variants. To support this, we organize the MalNet dataset, consisting of over a million entries of Android malware data collected over a decade, in chronological order. We first adapt state-of-the-art CIL approaches to meet TIML's requirements, serving as baseline methods. Then, we propose a novel multimodal TIML approach that leverages multiple malware modalities for improved performance. Extensive evaluations show that our TIML approaches outperform traditional CIL methods and demonstrate the feasibility of periodically updating malware classifiers at a low cost. This process is efficient and requires minimal storage and computational resources, with only a slight dip in performance compared to full retraining with historical data.

A phylogenomic tree of wood-warblers (Aves: Parulidae): Dealing with good, bad, and ugly samples.

The New World warblers (Parulidae) are a model group for ecological and evolutionary analyses. However, current phylogenetic relationships across this family are based upon few loci. Here we use ultraconserved elements (UCEs) to estimate a rigorous species-level phylogeny for the family. As is true for many groups, high-quality tissues were unavailable for some taxa. Thus, we explored methods for incorporating sequences derived from historical (toe pad) samples to expand the phylogenetic datasets. We recovered an average of 4,186 UCE loci and mitochondrial bycatch data (supplemented with published mitochondrial data) from 96 % of all currently recognized species. We found that the UCE phylogeny built with alignments with less than 70 % of gaps and ambiguities recovered the most robust phylogenetic relationships for this family, representing 101 species. Using this phylogeny as a topological backbone and adding ten fair quality "bad" samples effectively generated an overall well supported phylogeny, representing 108 species (∼90 % of all species). Based on this tree, we then added in seven poor quality "ugly" samples and six of those were placed within their expected genera. We also explored the phylogenetic positions of the likely extinct Leucopeza semperi and the endangered Catharopeza bishopi where limited data was obtained. Overall, taxonomic placements in our UCE trees largely correspond to previously published studies with the recovery of all currently recognized genera as monophyletic except for Basileuterus which was rendered paraphyletic by B. lachrymosus. Our study provides insights in understanding the phylogenetic relationships of a model Passeriformes family and outlines effective practices for managing sparse genomic data sourced from historical museum specimens. Variable topological arrangements across datasets and analyses reflect the evolutionary complexity of this group and provide future topics for in-depth studies.

Just-in-time framework for robust soft sensing based on robust variational autoencoder

Modeling with high-dimensional data subject to abnormal observations have always been a practical interest. In this paper, under the just-in-time learning (JITL) framework, a robust soft sensor modeling approach is developed based on robust Variational Autoencoder (VAE). Unlike the vanilla VAE that extracts features from the given dataset under the Gaussian prior assumption, robust VAE employs Student’s t-distribution as prior distribution to handle abnormal data. Under assumption of the Student’s t-prior, the proposed robust VAE model is capable of describing collected data contaminated with outliers. Once the robust VAE model is trained, each robust feature variable in the latent space can be determined. Subsequently, similarity measure is calculated using robust Kullback-Leibler divergence between two Student’s t-distributions, that is, the distribution of a new data sample and that of each historical data sample. After completing similarity measurement for a query sample, the weights for input-output historical data can be determined. Based on these weighted historical data samples, a robust probabilistic principal component regression (PPCR) is utilized to perform local modeling for prediction. Numerical simulations, including the Tennessee Eastman and Penicillin fermentation benchmark processes, are utilized to validate the proposed JITL-based robust soft sensor modeling method.

A Snakemake Toolkit for the Batch Assembly, Annotationand Phylogenetic Analysis of Mitochondrial Genomes and Ribosomal Genes From Genome Skims of Museum Collections.

Low coverage 'genome-skims' are often used to assemble organelle genomes and ribosomal gene sequences for cost-effective phylogenetic and barcoding studies. Natural history collections hold invaluable biological information, yet poor preservation resulting in degraded DNA often hinders polymerase chain reaction-based analyses. However, it is possible to generate libraries and sequence the short fragments typical of degraded DNA to generate genome-skims from museum collections. Here we introduce a snakemake toolkit comprised of three pipelines skim2mito, skim2rrna and gene2phylo, designed to unlock the genomic potential of historical museum specimens using genome skimming. Specifically, skim2mito and skim2rrna perform the batch assembly, annotation and phylogenetic analysis of mitochondrial genomes and nuclear ribosomal genes, respectively, from low-coverage genome skims. The third pipeline gene2phylo takes a set of gene alignments and performs phylogenetic analysis of individual genes, partitioned analysis of concatenated alignments and a phylogenetic analysis based on gene trees. We benchmark our pipelines with simulated data, followed by testing with a novel genome skimming dataset from both recent and historical solariellid gastropod samples. We show that the toolkit can recover mitochondrial and ribosomal genes from poorly preserved museum specimens of the gastropod family Solariellidae, and the phylogenetic analysis is consistent with our current understanding of taxonomic relationships. The generation of bioinformatic pipelines that facilitate processing large quantities of sequence data from the vast repository of specimens held in natural history museum collections will greatly aid species discovery and exploration of biodiversity over time, ultimately aiding conservation efforts in the face of a changing planet.

Sequencing RNA from old, dried specimens reveals past viromes and properties of long-surviving RNA.

Recovery of virus sequences from old samples provides an opportunity to study virus evolution and reconstruct historic virus-host interactions. Studies of old virus sequences have mainly relied on DNA or on RNA from fixed or frozen samples. The millions of specimens in natural history museums represent a potential treasure trove of old virus sequences, but it is not clear how well RNA survives in old samples. We experimentally assessed the stability of RNA in insects stored dry at room temperature over 72 weeks. Although RNA molecules grew fragmented, RNA yields remained surprisingly constant. RT-qPCR of host and virus RNA showed minimal differences between dried and frozen specimens. To assess RNA survival in much older samples we acquired Drosophila specimens from North American entomological collections. We recovered sequences from known and novel viruses including several coding complete virus genomes from a fly collected in 1908. We found that the virome of D. melanogaster has changed little over the past century. Galbut virus, the most prevalent virus infection in contemporary D. melanogaster , was also the most common in historic samples. Finally, we investigated the genomic and physical features of surviving RNA. RNA that survived was fragmented, chemically damaged, and preferentially double stranded or contained in ribonucleoprotein complexes. This showed that RNA - especially certain types of RNA - can survive in biological specimens over extended periods in the absence of fixation or freezing and confirms the utility of dried specimens to provide a clearer understanding of virus evolution.

Indigenous Australians, genomics, and the law

This article utilises three key characteristics of human genetic information—namely, its ubiquitous nature, its familial relationships and its predictive capacity—to explore how such research continues to exacerbate existing health inequalities for Indigenous Australians. By utilising substantive equality as its theoretical framework, this article explores key regulatory issues as follows: first, and regarding genetic information’s ubiquity, the article discusses how property laws in Australia fail to adequately protect Indigenous Australians from unauthorised usage of historical DNA samples; second, the familial nature of genetic information can leave Indigenous Australian’s liable to hyper-precise genetic definitions of Aboriginality, leading to a potentially adverse impact on claims of Native Title, due to the application of a biological definition to something which has always been more contextual and flexible; finally, the predictive element of genetic information is explored, and it is suggested that without proper regulation, could lead to increased genetic discrimination.

Sequencing of historic samples provides complete coding sequences of chicken calicivirus from the United States.

Here, we report the coding-complete genomic sequences of two chicken caliciviruses from US poultry flocks in 2003 and 2004. They show the same genomic organization as that of other members of the Bavovirus genus and have the highest nucleotide identity (~88%) with strains from clinically normal chickens from Germany in 2004 and Netherlands in 2019.

Influence of the painting medium on the alteration process of smalt in oil paintings studied using combined K and Co K-edge XANES

This study investigates the alteration processes affecting the smalt pigment in historical artworks through a combination of analytical techniques including X-ray Absorption Near Edge Structure (XANES) spectroscopy at the potassium (K) and cobalt (Co) K-edges, coupled with scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM-EDX) and micro X-ray fluorescence elemental mapping (µ-XRF). Laboratory mock-up samples prepared with different oil binding media were artificially aged, revealing varying rates of smalt degradation. µ-XANES analyses at the K K-edge provided grain-scale insights into smalt alteration, highlighting the influence of binding media composition on degradation kinetics. Crossed clustering data analysis over K µ-XANES acquired on both model samples and historical cross-sections corroborated findings and identified distinct spectral signatures associated with different stages of smalt degradation. Furthermore, identification of potential transformation products such as potassium alum in historical samples emphasized the dynamic nature of pigment alteration processes.

Genomics of historical museum collections clarifies species diversity in Cuban hutias (Capromys)

Abstract Specimen-based taxonomic research is essential for understanding diversity and setting management frameworks for threatened mammal faunas, and ancient DNA techniques are increasingly used to extract information from taxonomically relevant historical specimens. The largest survivors of the depleted Caribbean mammal fauna are hutias in the genus Capromys, which is usually interpreted as containing a single species, C. pilorides. Previous studies have demonstrated genetic differentiation of Capromys populations across Cuba, but infrageneric species diversity and nomenclature remain unclear. We conducted ancient DNA analysis of historical Capromys samples using cytochrome b and complete mitogenome data sets, and including the 19th-century holotypes of 2 species now considered synonyms, C. fournieri and C. geayi. Our analyses identify distinct western and central/eastern Capromys clades that diverged 1.75 Mya based upon mitogenome data. These clades are separated by the Havana–Matanzas Channel, which represented a barrier to dispersal throughout the Neogene–Quaternary. Divergence date comparisons with other hutia species provide support for interpreting divergence between Capromys populations as species-level differentiation. Although we were unable to yield amplifiable DNA from the C. fournieri holotype, our analyses confidently assign the C. geayi holotype to the western Capromys clade. We therefore recognize 2 extant Capromys species: C. geayi (western Cuba) and C. pilorides (central/eastern Cuba and Cayman Islands).

Stock identification of sympatric Atlantic cod populations in the Gulf of Maine and mixed stock fishery analysis using otolith-based techniques

Sympatric populations of Atlantic cod with distinct spawning times in winter and spring have been identified within the Gulf of Maine. A new western Gulf of Maine stock assessment unit in U.S. waters lumps winter and spring spawning populations into a single stock unit and future monitoring and assessment of their abundance will require mixed stock analysis. The goal of this study was to evaluate the utility of otolith-based stock identification techniques to discriminate spawning populations. Significant differences in otolith structure and microchemistry were identified between winter and spring spawners with the highest degree of classification accuracy based on both features. Mixed stock analysis applied to fishery samples of unknown origin indicated the contemporary (2015-2016) commercial fishery is dominated by winter spawners. Exploratory classification of historical fishery samples suggested a change over time with spring and winter spawners present in near equal proportion in the early 1990s and winter spawners dominating in the early 1980s. Otolith-based stock composition analysis has the potential to support monitoring and assessment of cod populations in the Gulf of Maine.

Spatial–Temporal Deviation Analysis for Multivariate Statistical Process Monitoring

ABSTRACTGiven that an effective process monitoring implementation should take both the spatial and temporal variations into account, a novel online process monitoring scheme based on a newly formulated algorithm titled as spatial–temporal deviation analysis (STDA) is proposed. Different from the mainstream process monitoring methods that focus on characterizing the spatial and/or temporal variation in the historical normal samples, the proposed STDA algorithm is designed to adaptively and timely train a pair of projecting vectors to uncover potential deviation in the spatial–temporal variation of online monitored samples, so as to guarantee consistently enhanced monitoring performance. Instead of utilizing a fixed projecting framework trained offline, the STDA algorithm is repeatedly executed once a newly measured sample become available for online monitoring. Therefore, the proposed STDA‐based method could consistently ensure its effectiveness for online fault detection, because a projecting framework targeted to revealing deviation in spatial–temporal variation is dynamically determined for different online monitoring samples in a timely manner. Finally, the salient monitoring performance achieved by the proposed STDA‐based approach is evaluated through comparisons with other counterparts.

Hats Off to Modeling! Profiling Early Synthetic Dyes on Historic Woolen Samples with ATR-FTIR Spectroscopy and Multivariate Curve Resolution-Alternating Least Square Algorithm.

This research focuses on analyzing wool samples dyed with synthetic dyes from the early 20th century. A methodology to identify and distinguish wool fibers dyed with azo, triphenylmethane, and xanthene dyes, which are no longer in use, using the ATR-FTIR spectra, is presented. Firstly, the dataset was subjected to PCA, which revealed the similarities and differences among the samples, illustrating a distribution pattern based on dye classes. MCR-ALS was employed to extract the spectral profiles of the dyed fibers, thereby enhancing the efficacy of the analytical techniques and extracting the comprehensive information from a single instrument. The combination of ATR-FTIR spectroscopy with chemometric methods, such as PCA and MCR-ALS, has proven to be an effective strategy for identifying and differentiating wool fibers dyed with early azo, triphenylmethane, and xanthene dyes. This approach has demonstrated particular effectiveness in enabling rapid analysis without requiring sampling or pretreatment. Moreover, the analysis is supported by thorough bibliographic research on these no longer used colorants. In order to maximize the potential of non-destructive spectroscopic techniques, such as ATR-FTIR, the approach used has proven to be crucial. This study underscores how chemometric techniques expand the capabilities of spectroscopy, extracting extensive information from a single instrument and aligning with the goals of cultural heritage analysis.

Oral microbial diversity in 18th century African individuals from South Carolina.

As part of the Anson Street African Burial Ground Project, we characterized the oral microbiomes of twelve 18th century African-descended individuals (Ancestors) from Charleston, South Carolina, USA, to study their oral health and diet. We found that their oral microbiome composition resembled that of other historic (18th-19th century) dental calculus samples but differed from that of modern samples,and was not influenced by indicators of oral health and wear observed in the dentition. Phylogenetic analysis of the oral bacteria, Tannerella forsythia and Pseudoramibacter alactolyticus, revealed varied patterns of lineage diversity and replacement in the Americas, with the Ancestors carrying strains similar to historic period Europeans and Africans. Functional profiling of metabolic pathways suggested that the Ancestors consumed a diet low in animal protein. Overall, our study reveals important insights into the oral microbial histories of African-descended individuals, particularly oral health and diet in colonial North American enslavement contexts.

A high-altitude population of Hyperboreomyzon polaris (Hirudinea: Glossiphoniidae) in Altai Mountains, South Siberia, Russia.

Hyperboreomyzon polaris Bolotov, Eliseeva, Klass & Kondakov, 2022 (Hirudinea: Glossiphoniidae) is an enigmatic freshwater leech that was recently described based on three specimens from two remote regions of the Eurasian Arctic, that is, the Kolguev Island and Putorana Plateau, Russia. Later on, misidentified historical samples of this species were discovered in the Hirudinea collection of Zoological Institute of the Russian Academy of Sciences (St. Petersburg, Russia). These samples were collected by Pavel G. Ignatov, a prominent Russian geographer and traveler, from a remote high-altitude area of the Altai Mountains (South Siberia) in 1901. To collect new samples from this population, we organized a field expedition to the same area (Lake Dzhulukul) in 2023. Molecular genetic data (COI and 18S rRNA) obtained from newly collected specimens revealed that they belong to H. polaris. Hence, this leech could be considered an Arctic-alpine species, the disjunctive range of which covers Arctic areas of Eurasia and Central Asian (South Siberian) mountains. We describe and illustrate living individuals of H. polaris for the first time, update its morphological diagnosis, present a life cycle reconstruction based on the frequency of four size classes in available samples. It is shown that this species prefers small lentic water bodies such as small lakes and lakelets. The crop content of a well-fed specimen from Altai contains DNA of the northern pintail Anas acuta Linnaeus (Aves: Anatidae), indicating that H. polaris feeds on blood of waterfowl. Our results indicate that Hyperboreomyzon may be considered a species adapted to cold high-latitude areas and mountain refugia.

Two-stage multi-objective distributionally robust operation optimization and benefits equalization of an off-grid type electric-hydrogen-ammonia-methanol coupling system

As the proportion of renewable energy has increased significantly, electric-hydrogen coupling technology has emerged as a pivotal strategy for optimizing the utilization of renewable energy resources. In particular, within the power and chemical sectors, the preparation of ammonia and methanol using electric-hydrogen coupling technology has emerged as the two principal avenues for the utilization of hydrogen energy. However, as a nascent technology, the preparation of ammonia and methanol by electric-hydrogen coupling is confronted with a multitude of challenges, including the considerable uncertainty surrounding the generation of renewable energy, the dearth of economic benefits, and the need to ensure a fair allocation of benefits among the various stakeholders. To enhance the risk resistance of the electric-hydrogen-ammonia-methanol coupling system (EHAMCS), improve the economic benefits, ensure the environmentality and stability of the system, and realize the fair distribution of benefits among the energy participants, this paper constructs a multi-objective distributionally robust optimization (DRO) and multi-dimensional benefits equilibrium model for the EHAMCS and performs a numerical analysis with an off-grid type EHAMCS as an example. The results demonstrate that: 1) The cooperative operation of the EHAMCS offers notable economic advantages. When compared with only pursuing economic benefits, under multi-objective optimization, the economic benefits of the coupling system can be reduced by 1.49 %, but the carbon emission can be reduced by 10.06 %, and the instability is reduced by 0.02, which can create derivative benefits. 2) The two-stage DRO model is an effective means of addressing the impact of system operation uncertainty and the affine strategy enables the rapid adjustment of the day-ahead dispatching plan, thereby balancing the power deviation. 3) The multi-dimensional factor benefit balancing scheme is more conducive to the participation of clean energy and downstream ammonia and methanol energy subsystems in cooperative operation and promotes the consumption of clean energy while improving the energy conversion value of the EHAMCS to increase economic benefits. 4) EHAMCS operators should adjust their operational strategies in time with market and policy signals, and select historical samples reasonably, so as to realize the balance of the DRO model in terms of economy, robustness, and practicality. The effectiveness of the model and the superiority of the EHAMCS are thus verified.

Museum-archived myctophids reveal decadal trends in microplastic and microfiber ingestion

Global plastic production has surged since the 1960s, resulting in the pervasive presence of microplastics in the environment, yet there is a substantial gap in understanding historical trends of plastic pollution in wildlife. Recent discoveries of significant microplastic contamination in fishes have sparked considerable contemporary advancements in analytical methods and hold the potential to fill gaps in historical trends. We measured the presence of microplastics in museum-archived myctophids (Stenobrachius leucopsarus, Diaphus theta, and Tarletonbeania crenularis) collected from 1962 to 2016, to determine if trends in contamination levels over time correspond with the rise in plastics production. Seventy particles were extracted from 57 of the 240 individuals (23.8 % average occurrence across the time series) consisting of primarily blue and black microfibers. Anthropogenically modified cellulose was the dominant material (87 %) identified through μFTIR analysis, with polypropylene and polyethylene particles occurring secondarily. Although the complete time series across a broad geographical range of the North Pacific did not reveal a significant temporal trend, myctophids collected in proximity to the U.S. west coast showed a trend towards increasing incidence of microplastic and microfiber ingestion over time (p ≤ 0.05). Using historical samples of species with higher ingestion levels and consistent collection locations would improve the reliability of future investigations.

GoEnrich: creating high quality genomic DNA resources from limited voucher specimen tissues or museum specimens of at-risk species for conservation-friendly use in the validation of environmental DNA assays

ObjectiveEnvironmental DNA (eDNA) methods are crucial for monitoring populations, particularly rare and cryptic species. For confident eDNA application, rigorous assay validation is required including specificity testing with genomic DNA (gDNA). However, this critical step is often difficult to achieve as obtaining fresh tissue samples from at-risk species can be difficult, highly limited, or impossible. Natural history museum collections could serve as a valuable and ethical voucher specimen resource for eDNA assay validation. The present study demonstrates the effectiveness of whole genome amplification (WGA) in providing enough gDNA to assemble high quality mitogenomes from which robust targeted eDNA assays can be designed.ResultsUsing fresh and historical museum tissue samples from six species spanning fish, birds, and mammals, we successfully developed a WGA method with an average yield of 380 to 1,268 ng gDNA per 20 µL reaction. This gDNA was used for whole genome shotgun sequencing and subsequent assembly of high quality mitogenomes using mtGrasp. These mitogenomes were then used to develop six new robust, targeted quantitative real time polymerase chain reaction-based eDNA assays and 200 ng WGA-enriched yielded satisfactory Cq values and near 100% detection frequencies for all assays tested. This approach offers a cost-effective and non-invasive alternative, streamlining eDNA research processes and aiding in conservation efforts.

Large language models for automatic equation discovery of nonlinear dynamics

Equation discovery aims to directly extract physical laws from data and has emerged as a pivotal research domain in nonlinear systems. Previous methods based on symbolic mathematics have achieved substantial advancements, but often require handcrafted representation rules and complex optimization algorithms. In this paper, we introduce a novel framework that utilizes natural language-based prompts to guide large language models (LLMs) in automatically extracting governing equations from data. Specifically, we first utilize the generation capability of LLMs to generate diverse candidate equations in string form and then evaluate the generated equations based on observations. The best equations are preserved and further refined iteratively using the reasoning capacity of LLMs. We propose two alternately iterated strategies to collaboratively optimize the generated equations. The first strategy uses LLMs as a black-box optimizer to achieve equation self-improvement based on historical samples and their performance. The second strategy instructs LLMs to perform evolutionary operations for a global search. Experiments are conducted on various nonlinear systems described by partial differential equations, including the Burgers equation, the Chafee–Infante equation, and the Navier–Stokes equation. The results demonstrate that our framework can discover correct equations that reveal the underlying physical laws. Further comparisons with state-of-the-art models on extensive ordinary differential equations showcase that the equations discovered by our framework possess physical meaning and better generalization capability on unseen data.