Published as a workshop paper at "Tackling Climate Change with Machine Learning", ICLR 2025 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 parametrized neural ordinary differential equations to address these limitations. Experiments on ocean mesoscale activity data show superior accuracy over existing baselines and improved computational efficiency compared to standard numerical simulations.

Learning a continuous and reliable representation of physical fields from sparse sampling is challenging and it affects diverse scientific disciplines. In a recent work, we present a novel model called MMGN (Multiplicative and Modulated Gabor Network) with implicit neural networks. In this work, we design additional studies leveraging explainability methods to complement the previous experiments and further enhance the understanding of latent representations generated by the model. The adopted methods are general enough to be leveraged for any latent space inspection. Preliminary results demonstrate the contextual information incorporated in the latent representations and their impact on the model performance. As a work in progress, we will continue to verify our findings and develop novel explainability approaches.

Reliably reconstructing physical fields from sparse sensor data is a challenge that frequently arises in many scientific domains. In practice, the process generating the data often is not understood to sufficient accuracy. Therefore, there is a growing interest in using the deep neural network route to address the problem. This work presents a novel approach that learns a continuous representation of the physical field using implicit neural representations (INRs). Specifically, after factorizing spatiotemporal variability into spatial and temporal components using the separation of variables technique, the method learns relevant basis functions from sparsely sampled irregular data points to develop a continuous representation of the data. In experimental evaluations, the proposed model outperforms recent INR methods, offering superior reconstruction quality on simulation data from a stateof-the-art climate model and a second dataset that comprises ultra-high resolution satellite-based sea surface temperature fields. Achieving accurate and comprehensive representation of complex physical fields is pivotal for tasks spanning system monitoring and control, analysis, and design. However, in a multitude of applications, encompassing geophysics (Reichstein et al., 2019), astronomy (Gabbard et al., 2022), biochemistry (Zhong et al., 2021), fluid mechanics (Deng et al., 2023), and others, using a sparse sensor network proves to be the most practical and effective solution. In meteorology and oceanography, variables such as atmospheric pressure, temperature, salinity/humidity, and wind/current velocity must be reconstructed from sparsely sampled observations. Currently, two distinct approaches are used to reconstruct full fields from sparse observations. Traditional physics model-based approaches are based on partial differential equations (PDEs). These approaches draw upon theoretical techniques to derive PDEs rooted in conservation laws and fundamental physical principles (Hughes, 2012). Yet, in complex systems such as weather (Brunton et al., 2016) and epidemiology (Massucci et al., 2016), deriving comprehensive models that are both sufficiently accurate and computationally efficient remains elusive.

Modeling is crucial to understanding the effect of greenhouse gases, warming, and ice sheet melting on the ocean. At the same time, ocean processes affect phenomena such as hurricanes and droughts. Parameters in the models that cannot be physically measured have a significant effect on the model output. For an idealized ocean model, we generated perturbed parameter ensemble data and trained surrogate neural network models. The neural surrogates accurately predicted the one-step forward dynamics, of which we then computed the parametric sensitivity.