Existing approaches such as PINN have limitations

The gap

Evidence profile

Sourced from the stated research gap and future-work section of the source papers, classified as general, drawn from work published between 2023 and 2026, spanning 4 journals. Those papers have been cited 7 times in total.

Supporting evidence — 4 representative gaps

• High-Fidelity Modeling of Stochastic Chemical Dynamics on Complex Manifolds: A Multiscale SIREN-PINN Framework for the Curvature-Perturbed Ginzburg–Landau Equation (2026) · Journal of Nonlinear Science · cited 1× · doi

  Conventional Physics-Informed Neural Networks (PINNs) suffer from spectral bias, failing to capture high-frequency fluctuations. The ability to predict how curvature perturbations influence stability regimes is critical for bridging the gap between idealized theoretical models and reality.

  generalstated research gapevidence 5/5
  Keywords: conventional physics-informed neural networks pinns suffer spectral bias
• Provably Convergent Physics-Informed Neural Operators for High-Dimensional Stochastic Partial Differential Equations (2026) · Zenodo (CERN European Organization for Nuclear Research) · doi

  Extending the framework to other types of partial differential equations. Developing more efficient and scalable algorithms for training Physics-Informed Neural Operators. Applying the framework to real-world problems in various scientific and engineering disciplines.

  generalfuture-work sectionevidence 5/5
  Keywords: extending framework other types partial differential equations developing
• Deep Physics Corrector: A physics enhanced deep learning architecture for solving stochastic differential equations (2023) · Journal of Computational Physics · cited 6× · doi

  Existing approaches such as PINN have limitations. Simulators are often computationally expensive and not applicable in real-time. There is a need for a approach that combines physics and deep learning to solve SDEs.

  generalstated research gapevidence 5/5
  Keywords: existing approaches pinn have limitations simulators often computationally
• A Spline-based Physics-Informed Numerical Scheme: Accurate Smooth Solutions for Differential Equations (2026) · arXiv

  Traditional solvers provide solutions only at specific nodal points or elements, and obtaining values between these points requires interpolation. The recent shift toward Physics-Informed Neural Networks (PINNs) has limitations such as requiring significant computational overhead and stochastic optimization.

  generalstated research gapevidence 5/5
  Keywords: traditional solvers provide solutions only specific nodal points

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