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Modifying solution viscosity is a key functional application of polymers, yet the interplay of molecular chemistry, polymer architecture, and intermolecular interactions makes tailoring precise rheological responses challenging. We introduce a computational framework coupling topology-aware generative machine learning, Gaussian process modeling, and multiparticle collision dynamics to design polymers yielding prescribed shear-rate-dependent viscosity profiles. Targeting thirty rheological profiles of varying difficulty, Bayesian optimization identifies polymers that satisfy all low- and most medium-difficulty targets by modifying topology and solvophobicity, with other variables fixed. In these regimes, we find and explain design degeneracy, where distinct polymers produce near-identical rheological profiles. However, satisfying high-difficulty targets requires extrapolation beyond the initial constrained design space; this is rationally guided by physical scaling theories. This integrated framework establishes a data-driven yet mechanistic route to rational polymer design. 

Revision: This revision includes four independent trajectory values of the ensemble averages of the mean squared radii of gyration and their standard deviations, which can be used to compute statistical measures such as the standard error. This distribution provides access to 18,450 configurations of coarse-grained polymers. The data is provided as a serialized object using the `pickle' Python module and in csv format. The data was compiled using Python version 3.8.  ReferencesThe specific applications and analyses of the data are described in 1.  Jiang, S.; Webb, M.A. "Physics-Guided Neural Networks for Transferable Prediction of Polymer Properties" DataThere are seven .pickle files that contain serialized Python objects. pattern_graph_data_*_*_rg_new.pickle: squared radii of gyration distribution from MD simulation. The number indicates the molecular weight range. rg2_baseline_*_new.pickle: squared radii of gyration distribution from Gaussian chain theoretical prediction. delta_data_v0314.pickle: torch_geometric training data. UsageTo access the data in the .pickle file, users can execute the following: # LOAD SIMULATION DATADATA_DIR = "your/custom/dir/"mw = 40 # or 90, 190 MWs filename = os.path.join(DATA_DIR, f"pattern_graph_data_{mw}_{mw+20}_rg_new.pickle")with open(filename, "rb") as handle:    graph = pickle.load(handle)    label = pickle.load(handle)    desc  = pickle.load(handle)    meta  = pickle.load(handle)    mode  = pickle.load(handle)    rg2_mean   = pickle.load(handle)    rg2_std    = pickle.load(handle) ** 0.5 # var # combine asymmetric and symmetric star polymerslabel[label == 'stara'] = 'star'# combine bottlebrush and other comb polymerslabel[label == 'bottlebrush'] = 'comb'  # LOAD GAUSSIAN CHAIN THEORETICAL DATAwith open(os.path.join(DATA_DIR, f"rg2_baseline_{mw}_new.pickle"), "rb") as handle:    rg2_mean_theo = pickle.load(handle)[:, 0]    rg2_std_theo = pickle.load(handle)[:, 0] graph: NetworkX graph representations of polymers. label: Architectural classes of polymers (e.g., linear, cyclic, star, branch, comb, dendrimer). desc: Topological descriptors (optional). meta: Identifiers for unique architectures (optional). mode: Identifiers for unique chemical patterns (optional). rg2_mean: Mean squared radii of gyration from simulations. rg2_std: Corresponding standard deviation from simulations. rg2_mean_theo: Mean squared radii of gyration from theoretical models. rg2_std_theo: Corresponding standard deviation from theoretical models. Help, Suggestions, Corrections?If you need help, have suggestions, identify issues, or have corrections, please send your comments to Shengli Jiang at sj0161@princeton.edu GitHubAdditional data and code relevant for this study is additionally accessible at https://github.com/webbtheosim/gcgnn 

Dataset Description This dataset contains 6710 structural configurations and solvophobicity values for topologically and chemically diverse coarse-grained polymer chains. Additionally, 480 polymers include shear-rate dependent viscosity profiles at 2 wt% polymer concentration.The data is provided as serialized objects using the pickle Python module.All files were generated using Python version 3.10. Data There are three pickle files containing serialized Python objects. Key files include: data_aug10.pickle  Contains the coarse-grained polymer dataset with 6710 entries.  Each entry includes: Polymer graph Squared radius of gyration (at lambda = 0). Solvophobicity (lambda). Bead count (N). Chain virial number (Xi). topo_param_visc.pickle   Shear-rate-dependent viscosity profiles of 480 polymer systems. target_curves.pickle  Contains 30 target viscosity profiles used for active learning. Usage To load the dataset stored in data_aug10.pickle, use the following code: import pickle with open("data_aug10.pickle", "rb") as handle:    (        (x_train, y_train, c_train, l_train, graph_train),        (x_valid, y_valid, c_valid, l_valid, graph_valid),        (x_test, y_test, c_test, l_test, graph_test),        NAMES,        SCALER,        SCALER_y,        le    ) = pickle.load(handle) x: node features for each polymer graph y: labels (e.g., predicted properties) c: topological class indices l: topological descriptors graph: NetworkX graphs representing polymer topology NAMES: list of topological class names SCALER: fitted scaler for topological descriptors (l) SCALER_y: fitted scaler for property labels (y) le: label encoder for topological class indices   To load the dataset stored in topo_param_visc.pickle, use the following code: import pickle with open("poly_data_ml.pickle", "rb") as handle:    desc_all, ps_all, curve_all, shear_rate, graph_all = pickle.load(handle) desc_all: topological descriptors for each polymer graph ps_all: fitted Carreau–Yasuda model parameters curve_all: fitted viscosity curves shear_rate: shear rates corresponding to each viscosity curve graph_all: polymer graphs represented as NetworkX objects   First 30: seed dataset Next 150: 5 iterations (30 each) from class-balanced space-filling Following 150: space-filling without class balancing Final 150: active learning samples    To load the dataset stored in target_curves.pickle, use the following code: import pickle with open("target_curves.pickle", "rb") as handle:    data = pickle.load(f) curves = data['curves']params = data['params']shear_rate = data["xx"]   curves: target viscosity curves used as design objectives params: Carreau–Yasuda model parameters fitted to the target curves shear_rate: shear rate values associated with the target curves     Help, Suggestions, Corrections?If you need help, have suggestions, identify issues, or have corrections, please send your comments to Shengli Jiang at sj0161@princeton.edu GitHubAdditional data and code relevant for this study is additionally accessible at https://github.com/webbtheosim/cg-topo-solv 

Phase separation in multicomponent mixtures is of significant interest in both fundamental research and technology. Although the thermodynamic principles governing phase equilibria are straightforward, practical determination of equilibrium phases and constituent compositions for multicomponent systems is often laborious and computationally intensive. Here, we present a machine-learning workflow that simplifies and accelerates phase-coexistence calculations. We specifically analyze capabilities of neural networks to predict the number, composition, and relative abundance of equilibrium phases of systems described by Flory-Huggins theory. We find that incorporating physics-informed material constraints into the neural network architecture enhances the prediction of equilibrium compositions compared to standard neural networks with minor errors along the boundaries of the stable region. However, introducing additional physics-informed losses does not lead to significant further improvement. These errors can be virtually eliminated by using machine-learning predictions as a warm-start for a subsequent optimization routine. This work provides a promising pathway to efficiently characterize multicomponent phase coexistence. 

Phase separation in multicomponent mixtures is of significant interest in both fundamental research and technology. Although the thermodynamic principles governing phase equilibria are straightforward, practical determination of equilibrium phases and constituent compositions for multicomponent systems is often laborious and computationally intensive. Here, we present a machine-learning workflow that simplifies and accelerates phase-coexistence calculations. We specifically analyze capabilities of neural networks to predict the number, composition, and relative abundance of equilibrium phases of systems described by Flory-Huggins theory. We find that incorporating physics-informed material constraints into the neural network architecture enhances the prediction of equilibrium compositions compared to standard neural networks with minor errors along the boundaries of the stable region. However, introducing additional physics-informed losses does not lead to significant further improvement. These errors can be virtually eliminated by using machine-learning predictions as a warm-start for a subsequent optimization routine. This work provides a promising pathway to efficiently characterize multicomponent phase coexistence. 

This dataset holds 1036 ternary phase diagrams and how points on the diagram phase separate if they do. The data is provided as a serialized object using the `pickle' Python module. The data was compiled using Python version 3.8.  ReferencesThe specific applications and analyses of the data are described in 1.  Dhamankar, S.; Jiang, S.; Webb, M.A. "Accelerating Multicomponent Phase-Coexistence Calculations with Physics-informed Neural Networks" UsageTo access the data in the .pickle file, users can execute the following: # LOAD SIMULATION DATADATA_DIR = "your/custom/dir/" filename = os.path.join(DATA_DIR, f"data_clean.pickle")with open(filename, "rb") as handle:    (x, y_c, y_r, phase_idx, num_phase, max_phase) = pickle.load(handle) x: Input x = (χ_AB, χ_BC, χ_AC, v_A, v_B, v_C, φ_A, φ_B) ∈ ℝ^8. y_c: Output one-hot encoded classification vector y_c ∈ ℝ^3. y_r: Output equilibrium composition and abundance vector y_r = (φ_A^α, φ_B^α, φ_A^β, φ_B^β, φ_A^γ, φ_B^γ, w^α, w^β, w^γ) ∈ ℝ^9. phase_idx: A single integer indicating which unique phase system it belongs to. num_phase: A single integer indicates the number of equilibrium phases the input splits into. max_phase: A single integer indicates the maximum number of equilibrium phases the system splits into. Help, Suggestions, Corrections?If you need help, have suggestions, identify issues, or have corrections, please send your comments to Shengli Jiang at sj0161@princeton.edu GitHubAdditional data and code relevant for this study is additionally accessible at hthttps://github.com/webbtheosim/ml-ternary-phase 

This distribution provides the code and reference data for the manuscript of "Understanding the interplay between electrocatalytic C(sp3)‒C(sp3) fragmentation and oxygenation reactions"