Generalizable Implicit Neural Representations via Parameterized Latent Dynamics for Baroclinic Ocean Forecasting

TL;DR

Forecasting mesoscale ocean dynamics under varying physical parameters is essential but computationally expensive. PINROD integrates implicit neural representations with parameterized neural ODEs to learn latent dynamics conditioned on the parameter vector $\u03bc$, enabling continuous-time and continuous-space predictions $u(t,x)$ on unstructured meshes. Its three-component design—an encoder, a PNODE with explicit parameter dependency, and a SIREN-based coordinate decoder—paired with a two-stage training regime, yields improved accuracy and efficiency over baselines on the SOMA dataset. This approach supports rapid, many-query, parameter-aware ocean forecasting, reducing reliance on costly high-resolution simulations for climate analysis and uncertainty quantification.

Abstract

Mesoscale ocean dynamics play a critical role in climate systems, governing heat transport, hurricane genesis, and drought patterns. However, simulating these processes at high resolution remains computationally prohibitive due to their nonlinear, multiscale nature and vast spatiotemporal domains. Implicit neural representations (INRs) reduce the computational costs as resolution-independent surrogates but fail in many-query scenarios (inverse modeling) requiring rapid evaluations across diverse parameters. We present PINROD, a novel framework combining dynamics-aware implicit neural representations with parameterized neural ordinary differential equations to address these limitations. By integrating parametric dependencies into latent dynamics, our method efficiently captures nonlinear oceanic behavior across varying boundary conditions and physical parameters. Experiments on ocean mesoscale activity data show superior accuracy over existing baselines and improved computational efficiency compared to standard numerical simulations.

Figures (5)

• Figure 1: The mean squared error (MSE) of temperature predictions over 29 days. FNO exhibits accumulating error due to its autoregressive strategy, while VCNeF and PINROD maintain more stable performance.
• Figure 2: Qualitative Comparison of Temperature Fields. Snapshots at $t=29$ for different depths ($z=0,7,13,19$). PINROD more accurately preserves fine-scale structures.
• Figure 3: Temperature field at $\boldsymbol{t=0}$.
• Figure 4: Temperature field at $\boldsymbol{t=9}$.
• Figure 5: Temperature field at $\boldsymbol{t=19}$.