Topology-aware Conv1D–LSTM for Streamflow simulating: Integrating Hodge Laplacian Features with Deep Sequential Learning

doi:10.21203/rs.3.rs-7502495/v1

Topology-aware Conv1D–LSTM for Streamflow simulating: Integrating Hodge Laplacian Features with Deep Sequential Learning

2025 · doi:10.21203/rs.3.rs-7502495/v1

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This paper studies rainfall–runoff streamflow forecasting by proposing a hybrid Conv1D–LSTM model that integrates Hodge Laplacian–derived algebraic-topological descriptors to encode higher-order connectivity of a river network. Using rainfall and discharge data from a five-station basin in southwest Iran, the authors compare Conv1D–LSTM–Hodge against conventional Conv1D–LSTM and other deep learning baselines, reporting improved performance (RMSE 0.74, MAE 0.56, NSE 0.89, R² 0.91) and better mid-to-high flow hydrograph behavior, with a stated tendency to slightly underestimate rare high peaks. The paper frames ensemble diagnostics as evidence of robust uncertainty representation without excessive heavy tails, but the abstract does not specify additional limitations beyond the difficulty of rare-event prediction. This paper does not explicitly discuss endometriosis or adenomyosis; it was included in the corpus via a keyword match in the upstream search index.

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Abstract

Abstract Reliable hydrological forecasting remains a central challenge in water resources management due to the nonlinear dynamics of rainfall–runoff processes and the complex spatial structure of river networks. While deep learning methods such as long short-term memory (LSTM) and convolutional neural networks (CNNs) have improved predictive capability by extracting sequential and local patterns, most existing models fail to explicitly account for the topological connectivity of catchments. To address this gap, novel hybrid framework that integrates Conv1D layers for local spatiotemporal feature extraction proposed, LSTM layers for long-term memory retention, and algebraic-topological descriptors derived from Hodge Laplacian decomposition to encode higher-order graph-based connectivity of the river network. The model was evaluated using rainfall and discharge records from a five-station basin in southwest Iran, with systematic comparison against conventional Conv1D–LSTM and standalone deep learning architectures. Results indicate that the Conv1D–LSTM–Hodge model achieves consistent improvements in accuracy, yielding RMSE = 0.74, MAE = 0.56, NSE = 0.89, and R² = 0.91, outperforming the baseline Conv1D–LSTM (RMSE = 0.95, NSE = 0.82, R² = 0.85). At lower to moderate flows, the model reproduces the hydrograph with minimal bias, while at high extremes it slightly underestimates peak discharges, consistent with the statistical difficulty of rare-event prediction. Importantly, the inclusion of Hodge features reduces scatter in mid-to-high discharge regimes by encoding gradient- and cycle-based flow structures, thereby enhancing both predictive reliability and structural consistency. Ensemble diagnostics (standard deviation = 0.98, variance = 0.96, range = 7.09, skewness = 0.12, kurtosis = 0.07, entropy = 5.86, CV ≈ 50) confirm robust uncertainty representation without excessive heavy tails, ensuring balanced forecasts. Beyond accuracy, the proposed model advances interpretability by linking algebraic topology with deep learning, bridging physical plausibility and statistical precision. These findings position the Conv1D–LSTM–Hodge framework as a promising data-driven tool for flood forecasting, reservoir operation, and drought preparedness, with broader implications for embedding graph-theoretic insights into hydrological machine learning.

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Topology-aware Conv1D–LSTM for Streamflow simulating: Integrating Hodge Laplacian Features with Deep Sequential Learning | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Topology-aware Conv1D–LSTM for Streamflow simulating: Integrating Hodge Laplacian Features with Deep Sequential Learning Hamid Ebrahimi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7502495/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract Reliable hydrological forecasting remains a central challenge in water resources management due to the nonlinear dynamics of rainfall–runoff processes and the complex spatial structure of river networks. While deep learning methods such as long short-term memory (LSTM) and convolutional neural networks (CNNs) have improved predictive capability by extracting sequential and local patterns, most existing models fail to explicitly account for the topological connectivity of catchments. To address this gap, novel hybrid framework that integrates Conv1D layers for local spatiotemporal feature extraction proposed, LSTM layers for long-term memory retention, and algebraic-topological descriptors derived from Hodge Laplacian decomposition to encode higher-order graph-based connectivity of the river network. The model was evaluated using rainfall and discharge records from a five-station basin in southwest Iran, with systematic comparison against conventional Conv1D–LSTM and standalone deep learning architectures. Results indicate that the Conv1D–LSTM–Hodge model achieves consistent improvements in accuracy, yielding RMSE = 0.74, MAE = 0.56, NSE = 0.89, and R² = 0.91, outperforming the baseline Conv1D–LSTM (RMSE = 0.95, NSE = 0.82, R² = 0.85). At lower to moderate flows, the model reproduces the hydrograph with minimal bias, while at high extremes it slightly underestimates peak discharges, consistent with the statistical difficulty of rare-event prediction. Importantly, the inclusion of Hodge features reduces scatter in mid-to-high discharge regimes by encoding gradient- and cycle-based flow structures, thereby enhancing both predictive reliability and structural consistency. Ensemble diagnostics (standard deviation = 0.98, variance = 0.96, range = 7.09, skewness = 0.12, kurtosis = 0.07, entropy = 5.86, CV ≈ 50) confirm robust uncertainty representation without excessive heavy tails, ensuring balanced forecasts. Beyond accuracy, the proposed model advances interpretability by linking algebraic topology with deep learning, bridging physical plausibility and statistical precision. These findings position the Conv1D–LSTM–Hodge framework as a promising data-driven tool for flood forecasting, reservoir operation, and drought preparedness, with broader implications for embedding graph-theoretic insights into hydrological machine learning. Streamflow forecasting Conv1D–LSTM hybrid Hodge Laplacian rainfall–runoff modeling deep learning uncertainty analysis algebraic topology hydrological prediction Full Text Cite Share Download PDF Status: Under Review Version 1 posted Editor invited by journal 16 Mar, 2026 Reviewers agreed at journal 30 Sep, 2025 Reviewers invited by journal 30 Sep, 2025 Editor assigned by journal 02 Sep, 2025 First submitted to journal 31 Aug, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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central challenge in water resources management due to the nonlinear dynamics of rainfall\u0026ndash;runoff processes and the complex spatial structure of river networks. While deep learning methods such as long short-term memory (LSTM) and convolutional neural networks (CNNs) have improved predictive capability by extracting sequential and local patterns, most existing models fail to explicitly account for the topological connectivity of catchments. To address this gap, novel hybrid framework that integrates Conv1D layers for local spatiotemporal feature extraction proposed, LSTM layers for long-term memory retention, and algebraic-topological descriptors derived from Hodge Laplacian decomposition to encode higher-order graph-based connectivity of the river network. The model was evaluated using rainfall and discharge records from a five-station basin in southwest Iran, with systematic comparison against conventional Conv1D\u0026ndash;LSTM and standalone deep learning architectures. Results indicate that the Conv1D\u0026ndash;LSTM\u0026ndash;Hodge model achieves consistent improvements in accuracy, yielding RMSE\u0026thinsp;=\u0026thinsp;0.74, MAE\u0026thinsp;=\u0026thinsp;0.56, NSE\u0026thinsp;=\u0026thinsp;0.89, and R\u0026sup2; = 0.91, outperforming the baseline Conv1D\u0026ndash;LSTM (RMSE\u0026thinsp;=\u0026thinsp;0.95, NSE\u0026thinsp;=\u0026thinsp;0.82, R\u0026sup2; = 0.85). At lower to moderate flows, the model reproduces the hydrograph with minimal bias, while at high extremes it slightly underestimates peak discharges, consistent with the statistical difficulty of rare-event prediction. Importantly, the inclusion of Hodge features reduces scatter in mid-to-high discharge regimes by encoding gradient- and cycle-based flow structures, thereby enhancing both predictive reliability and structural consistency. 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