4FN&WBM >ɽ ղܾࡦ • ݴޠϞσϧʹجͮ͘ख๏Λ࠾༻͠ɼϓϩηεؔ࿈σʔληοτͰϑΝΠϯνϡʔχϯά͢Δɽ มఆٛநग़ख๏ͷ։ൃ ೖྗ The heat of the reaction values (∆H𝑟 ) are given alongside the reactions. The heat of the reaction values ग़ྗ จ มఆٛ ϓϩηεؔ࿈σʔληοτͰ ϑΝΠϯνϡʔχϯάͨ͠Ϟσϧ The heat of the reaction values (∆𝐻r ) are given alongside the reactions. มه߸ มఆٛ 34/75
ఏҊख๏͕ࣦഊ͢Δέʔε The kinetic coefficients correspond to the Arrhenius equation: 𝑘4 = 𝐴4𝑒5( ⁄ 8! 9",$); 𝑖 = 1, 2, … , 6, where 𝐴4 is the frequency factor … ਖ਼ղ The parameter 𝛼 accounts for the mass of seed crystals charged into the crystallizer at 𝑡 = 0 and scales 𝑓(𝑥) accordingly. ਖ਼ղ 39/75
equation in one EG has the equivalent equation in the other EG EG: 数式群（Equation group） Eliminates within-group shared variables not included in between-group shared variables END Two EGs have the same variables YES NO [Kato+, Sci. Rep., 2023] 47/75
Lorenz system.” Text description System observation LLM Describe the following data: VLM Describe the following plot: Prompt You are an expert at using the SINDy method for discovering physical laws. You are required to … Think step-by-step … Code library doc … Practical tips … System User High performing examples … User RAG User Previous attempts + scores … LLM Optimization Score model Train score: 0.97, Test score: 0.87 User Human feedback Consider also … from pysindy.feature_library import * import numpy as np custom_lib =[lambda x: np.exp(x)] feature_library = ConcatLibrary([ FourierLibrary(n_frequencies=2), PolynomialLibrary(degree=2, include_interaction=True), CustomLibrary(library_functions=custom_lib), ]) Test data Optimizer Feature library • ݕࡧ֦ுੜʢ3"(ʣɼ--.ɼࢹ֮ݴޠϞσϧʢ7-.ʣΛ׆༻ͯ͠ɼ 4*/%Zద༻ʹඞཁͳϥΠϒϥϦͱ࠷దԽثʢPQUJNJ[FSʣΛબ͢Δख๏ɽ • ϕϯνϚʔΫʹରͯ͠ߴ͍ੑೳΛୡ͍ͯ͠Δɽ ؔ࿈ݚڀɿ"*,IXBSJ[NJ<.PXFSBOE#PV"NNBS BS9JW > 66/75
## Domain: {system type} ### State Variables - {state variable}: {variable description} - ... ### Input Variables - {input variable}: {variable description} - ... ### Constraints - Maximum polynomial degree: {max degree} - Allowed operators: {allowed operators} ### Experimental Background {experimental background} - ... Physical constraints for constitutive equations: - Spatial symmetry sign-reversal symmetry): Under shear reversal (κ_xy →-κ_xy), the constitutive equations must respect the corresponding symmetry of the physical system. - As a consequence, even-order terms of the velocity gradient appearing alone (e.g., κ_xy^2 κ_xy^4 without coupling to stress) are not physically admissible. - The velocity gradient κ_xy may only appear in symmetry-consistent combinations, such as convective coupling terms with stress components. ... 69/75
identification of nonlinear dynamics (SINDy). Your task is to generate candidate library terms for discovering governing equations from time-series data. {output by Domain Curator} ## Task Generate a comprehensive list of candidate library terms that could appear in the governing equations for this system. ## Guidelines 1. Include fundamental terms: Constants (1), linear terms, and polynomial products up to degree {max degree} 2. ... ## Expected Output Format Return a JSON object with: ... ## Variables Available {variable list} Generate the candidate library terms now. -JCSBSZ(FOFSBUPSͷઃܭ ## Domain: {system type} ### State Variables - {state variable}: {variable description} - ... ### Input Variables - {input variable}: {variable description} - ... ### Constraints - Maximum polynomial degree: {max degree} - Allowed operators: {allowed operators} ### Experimental Background {experimental background} 70/75
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