We introduce TAM-RL (Task Aware Modulation using Representation Learning), a novel multimodal meta-learning framework for few-shot learning in heterogeneous systems, designed for science and engineering problems where entities share a common underlying forward model but exhibit heterogeneity due to entity-specific characteristics. TAM-RL leverages an amortized training process with a modulation network and a base network to learn task-specific modulation parameters, enabling efficient adaptation to new tasks with limited data. We evaluate TAM-RL on two real-world environmental datasets: Gross Primary Product (GPP) prediction and streamflow forecasting, demonstrating significant improvements over existing meta-learning methods. On the FLUXNET dataset, TAM-RL improves RMSE by 18.9% over MMAML with just one month of few-shot data, while for streamflow prediction, it achieves an 8.21% improvement with one year of data. Synthetic data experiments further validate TAM-RL’s superior performance in heterogeneous task distributions, outperforming the baselines in the most heterogeneous setting. Notably, TAM-RL offers substantial computational efficiency, with at least 3x faster training times compared to gradient-based meta-learning approaches while being much simpler to train due to reduced complexity. Ablation studies highlight the importance of pretraining and adaptation mechanisms in TAM-RL’s performance.

Accurate long-term predictions are the foundations for many machine learning applications and decision-making processes. Traditional time series approaches for prediction often focus on either autoregressive modeling, which relies solely on past observations of the target “endogenous variables”, or forward modeling, which considers only current covariate drivers “exogenous variables”. However, effectively integrating past endogenous and past exogenous with current exogenous variables remains a significant challenge. In this paper, we propose ExoTST, a novel transformer-based framework that effectively incorporates current exogenous variables alongside past context for improved time series prediction. To integrate exogenous information efficiently, ExoTST leverages the strengths of attention mechanisms and introduces a novel cross-temporal modality fusion module. This module enables the model to jointly learn from both past and current exogenous series, treating them as distinct modalities. By considering these series separately, ExoTST provides robustness and flexibility in handling data uncertainties that arise from the inherent distribution shift between historical and current exogenous variables. Extensive experiments on real-world carbon flux datasets and time series benchmarks demonstrate ExoTST's superior performance compared to state-of-the-art baselines, with improvements of up to 10% in prediction accuracy. Moreover, ExoTST exhibits strong robustness against missing values and noise in exogenous drivers, maintaining consistent performance in real-world situations where these imperfections are common.

Many environmental systems (e.g., hydrology basins) can be modeled as entity whose response (e.g., streamflow) depends on drivers (e.g., weather) conditioned on their characteristics (e.g., soil properties). We introduce Entity-aware Conditional Variational Inference (EA-CVI), a novel probabilistic inverse modeling approach, to deduce entity characteristics from observed driver-response data. EA-CVI infers probabilistic latent representations that can accurately predict response for diverse entities, particularly in out-of-sample few-shot settings. EA-CVI's latent embeddings encapsulate diverse entity characteristics within compact, low-dimensional representations. EA-CVI proficiently identifies dominant modes of variation in responses and offers the opportunity to infer a physical interpretation of the underlying attributes that shape these responses. EA-CVI can also generate new data samples by sampling from the learned distribution, making it useful in zero-shot scenarios. EA-CVI addresses the need for uncertainty estimation, particularly during extreme events, rendering it essential for data-driven decision-making in real-world applications. Extensive evaluations on a renowned hydrology benchmark dataset, CAMELS-GB, validate EA-CVI's abilities.

Time series modeling, a crucial area in science, often encounters challenges when training Machine Learning (ML) models like Recurrent Neural Networks (RNNs) using the conventional mini-batch training strategy that assumes independent and identically distributed (IID) samples and initializes RNNs with zero hidden states. The IID assumption ignores temporal dependencies among samples, resulting in poor performance. This paper proposes the Message Propagation Through Time (MPTT) algorithm to effectively incorporate long temporal dependencies while preserving faster training times relative to the stateful algorithms. MPTT utilizes two memory modules to asynchronously manage initial hidden states for RNNs, fostering seamless information exchange between samples and allowing diverse mini-batches throughout epochs. MPTT further implements three policies to filter outdated and preserve essential information in the hidden states to generate informative initial hidden states for RNNs, facilitating robust training. Experimental results demonstrate that MPTT outperforms seven strategies on four climate datasets with varying levels of temporal dependencies.

Accurate long-term predictions are the foundations for many machine learning applications and decision-making processes. However, building accurate long-term prediction models remains challenging due to the limitations of existing temporal models like recurrent neural networks (RNNs), as they capture only the statistical connections in the training data and may fail to learn the underlying dynamics of the target system. To tackle this challenge, we propose a novel machine learning model based on Koopman operator theory, which we call Koopman Invertible Autoencoders (KIA), that captures the inherent characteristic of the system by modeling both forward and backward dynamics in the infinite-dimensional Hilbert space. This enables us to efficiently learn low-dimensional representations, resulting in more accurate predictions of long-term system behavior. Moreover, our method’s invertibility design enforces reversibility and consistency in both forward and inverse operations. We illustrate the utility of KIA on pendulum and climate datasets, demonstrating 300% improvements in long-term prediction capability for pendulum while maintaining robustness against noise. Additionally, our method demonstrates the ability to better comprehend the intricate dynamics of the climate system when compared to existing Koopman-based methods.

Rapid advancement in inverse modeling methods have brought into light their susceptibility to imperfect data. This has made it imperative to obtain more explainable and trustworthy estimates from these models. In hydrology, basin characteristics can be noisy or missing, impacting streamflow prediction. We propose a probabilistic inverse model framework that can reconstruct robust hydrology basin characteristics from dynamic input weather driver and streamflow response data. We address two aspects of building more explainable inverse models, uncertainty estimation (uncertainty due to imperfect data and imperfect model) and robustness. This can help improve the trust of water managers, handling of noisy data and reduce costs. We also propose an uncertainty based loss regularization that offers removal of 17% of temporal artifacts in reconstructions, 36% reduction in uncertainty and 4% higher coverage rate for basin characteristics. The forward model performance (streamflow estimation) is also improved by 6% using these uncertainty learning based reconstructions.

Machine Learning is beginning to provide state-of-the-art performance in a range of environmental applications such as streamflow prediction in a hydrologic basin. However, building accurate broad-scale models for streamflow remains challenging in practice due to the variability in the dominant hydrologic processes, which are best captured by sets of process-related basin characteristics. Existing basin characteristics suffer from noise and uncertainty, among many other things, which adversely impact model performance. To tackle the above challenges, in this paper, we propose a novel Knowledge-guided Self-Supervised Learning (KGSSL) inverse framework to extract system characteristics from driver(input) and response(output) data. This first-of-its-kind framework achieves robust performance even when characteristics are corrupted or missing. We evaluate the KGSSL framework in the context of stream flow modeling using CAMELS (Catchment Attributes and MEteorology for Large-sample Studies) which is a widely used hydrology benchmark dataset. Specifically, KGSSL outperforms baseline by 16% in predicting missing characteristics. Furthermore, in the context of forward modelling, KGSSL inferred characteristics provide a 35% improvement in performance over a standard baseline when the static characteristic are unknown.