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ARXIV:2604.05652 · SCIENTIFIC ML · SUBMITTED 08 APR · 03:21 UTC · FRESHNESS UNKNOWN
ARXIV:2604.05652SCIENTIFIC MLSUBMITTED 08 APR · 03:21 UTCFRESHNESS UNKNOWNPrashant Kumar · Rajesh Ranjan · arXiv
A Domain-Decomposed and Shifted Physics-Informed Neural Network (DDS-PINN) framework for complex fluid flows that resolves multiscale interactions with minimal supervision.
Opportunity summary
Pain A Domain-Decomposed and Shifted Physics-Informed Neural Network (DDS-PINN) framework for complex fluid flows that resolves multiscale interactions with minimal supervision.
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A Domain-Decomposed and Shifted Physics-Informed Neural Network (DDS-PINN) framework for complex fluid flows that resolves multiscale interactions with minimal supervision. Predicting such phenomena remains a formidable challenge in scientific machine learning, particularly regarding convergence…
Fluid flows are governed by the nonlinear Navier-Stokes equations, which can manifest multiscale dynamics even from predictable initial conditions. Predicting such phenomena remains a formidable challenge in scientific machine learning, particularly regarding convergence speed,…
ScienceToStartup currently rates this 4.0/10 on the public viability pass. In complex fluid flows, these challenges are exacerbated by long-range spatial dependencies arising from distant boundary conditions, which typically necessitate extensive supervision data to…
Scientific ML moved forward this cycle; last verified April 2026. Public score 4.0/10. Production flags indicate code availability.
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A Domain-Decomposed and Shifted Physics-Informed Neural Network (DDS-PINN) framework for complex fluid flows that resolves multiscale interactions with minimal supervision.
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10.48550/arXiv.2604.05652A Domain-Decomposed and Shifted Physics-Informed Neural Network (DDS-PINN) framework for complex fluid flows that resolves multiscale interactions with minimal supervision.
Abstract
Fluid flows are governed by the nonlinear Navier-Stokes equations, which can manifest multiscale dynamics even from predictable initial conditions. Predicting such phenomena remains a formidable challenge in scientific machine learning, particularly regarding convergence speed, data requirements, and solution accuracy. In complex fluid flows, these challenges are exacerbated by long-range spatial dependencies arising from distant boundary conditions, which typically necessitate extensive supervision data to achieve acceptable results. We propose the Domain-Decomposed and Shifted Physics-Informed Neural Network (DDS-PINN), a framework designed to resolve such multiscale interactions with minimal supervision. By utilizing localized networks with a unified global loss, DDS-PINN captures global dependencies while maintaining local precision. The robustness of the approach is demonstrated across a suite of benchmarks, including a multiscale linear differential equation, the nonlinear Burgers' equation, and data-free Navier-Stokes simulations of flat-plate boundary layers. Finally, DDS-PINN is applied to the computationally challenging backward-facing step (BFS) problem; for laminar regimes (Re = 100), the model yields results comparable to computational fluid dynamics (CFD) without the need for any data, accurately predicting boundary layer thickness, separation, and reattachment lengths. For turbulent BFS flow at Re = 10,000, the framework achieves convergence to O(10^-4) using only 500 random supervision points (< 0.3 % of the total domain), outperforming established methods like Residual-based Attention-PINN in accuracy. This approach demonstrates strong potential for the super-resolution of complex turbulent flows from sparse experimental measurements.
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PROBLEM
A Domain-Decomposed and Shifted Physics-Informed Neural Network (DDS-PINN) framework for complex fluid flows that resolves multiscale interactions with minimal supervision. Predicting such phenomena remains a formidable challenge in scientific machine learning, particularly rega...
METHOD
Fluid flows are governed by the nonlinear Navier-Stokes equations, which can manifest multiscale dynamics even from predictable initial conditions. Predicting such phenomena remains a formidable challenge in scientific machine learning, particularly regarding convergence speed,...
RESULT
ScienceToStartup currently rates this 4.0/10 on the public viability pass. In complex fluid flows, these challenges are exacerbated by long-range spatial dependencies arising from distant boundary conditions, which typically necessitate extensive supervision data to achieve acce...
WHY NOW
Scientific ML moved forward this cycle; last verified April 2026. Public score 4.0/10. Production flags indicate code availability.
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A Domain-Decomposed and Shifted Physics-Informed Neural Network (DDS-PINN) framework for complex fluid flows that resolves multiscale interactions with minimal supervision. Predicting such phenomena remains a formidable challenge in scientific machine learning, particularly regarding convergence speed, data requirements, and solution accuracy.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Fluid flows are governed by the nonlinear Navier-Stokes equations, which can manifest multiscale dynamics even from predictable initial conditions. Predicting such phenomena remains a formidable challenge in scientific machine learning, particularly regarding convergence speed, data requirements, and solution accuracy.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
ScienceToStartup currently rates this 4.0/10 on the public viability pass. In complex fluid flows, these challenges are exacerbated by long-range spatial dependencies arising from distant boundary conditions, which typically necessitate extensive supervision data to achieve acceptable results. Code availability is flagged in the production record; the public repository link still needs proof alignment.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Scientific ML moved forward this cycle; last verified April 2026. Public score 4.0/10. Production flags indicate code availability.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
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A Domain-Decomposed and Shifted Physics-Informed Neural Network (DDS-PINN) framework for complex fluid flows that resolves multiscale interactions with minimal supervision.
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