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Register a new userForecasting Sequential Data using Consistent Koopman Autoencoders
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Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering an alternative for processing nonlinear dynamical systems. In this work, we propose a novel Consistent Koopman Autoencoder model which, unlike the majority of existing work, leverages the forward and backward dynamics. Key to our approach is a new analysis which explores the interplay between consistent dynamics and their associated Koopman operators. Our network is directly related to the derived analysis, and its computational requirements are comparable to other baselines. We evaluate our method on a wide range of high-dimensional and short-term dependent problems, and it achieves accurate estimates for significant prediction horizons, while also being robust to noise.
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The ability to extract generative parameters from high-dimensional fields of data in an unsupervised manner is a highly desirable yet unrealized goal in computational physics. This work explores the use of variational autoencoders (VAEs) for non-linear dimension reduction with the aim of disentangling the low-dimensional latent variables to identify independent physical parameters that generated the data. A disentangled decomposition is interpretable and can be transferred to a variety of tasks including generative modeling, design optimization, and probabilistic reduced order modelling. A major emphasis of this work is to characterize disentanglement using VAEs while minimally modifying the classic VAE loss function (i.e. the ELBO) to maintain high reconstruction accuracy. Disentanglement is shown to be highly sensitive to rotations of the latent space, hyperparameters, random initializations and the learning schedule. The loss landscape is characterized by over-regularized local minima which surrounds desirable solutions. We illustrate comparisons between disentangled and entangled representations by juxtaposing learned latent distributions and the true generative factors in a model porous flow problem. Implementing hierarchical priors (HP) is shown to better facilitate the learning of disentangled representations over the classic VAE. The choice of the prior distribution is shown to have a dramatic effect on disentanglement. In particular, the regularization loss is unaffected by latent rotation when training with rotationally-invariant priors, and thus learning non-rotationally-invariant priors aids greatly in capturing the properties of generative factors, improving disentanglement. Some issues inherent to training VAEs, such as the convergence to over-regularized local minima are illustrated and investigated, and potential techniques for mitigation are presented.
Production forecasting is a key step to design the future development of a reservoir. A classical way to generate such forecasts consists in simulating future production for numerical models representative of the reservoir. However, identifying such models can be very challenging as they need to be constrained to all available data. In particular, they should reproduce past production data, which requires to solve a complex non-linear inverse problem. In this paper, we thus propose to investigate the potential of machine learning algorithms to predict the future production of a reservoir based on past production data without model calibration. We focus more specifically on robust online aggregation, a deterministic approach that provides a robust framework to make forecasts on a regular basis. This method does not rely on any specific assumption or need for stochastic modeling. Forecasts are first simulated for a set of base reservoir models representing the prior uncertainty, and then combined to predict production at the next time step. The weight associated to each forecast is related to its past performance. Three different algorithms are considered for weight computations: the exponentially weighted average algorithm, ridge regression and the Lasso regression. They are applied on a synthetic reservoir case study, the Brugge case, for sequential predictions. To estimate the potential of development scenarios, production forecasts are needed on long periods of time without intermediary data acquisition. An extension of the deterministic aggregation approach is thus proposed in this paper to provide such multi-step-ahead forecasts.
Accurate short-term load forecasting is essential for efficient operation of the power sector. Predicting load at a fine granularity such as individual households or buildings is challenging due to higher volatility and uncertainty in the load. In aggregate loads such as at grids level, the inherent stochasticity and fluctuations are averaged-out, the problem becomes substantially easier. We propose an approach for short-term load forecasting at individual consumers (households) level, called Forecasting using Matrix Factorization (FMF). FMF does not use any consumers demographic or activity patterns information. Therefore, it can be applied to any locality with the readily available smart meters and weather data. We perform extensive experiments on three benchmark datasets and demonstrate that FMF significantly outperforms the computationally expensive state-of-the-art methods for this problem. We achieve up to 26.5% and 24.4 % improvement in RMSE over Regression Tree and Support Vector Machine, respectively and up to 36% and 73.2% improvement in MAPE over Random Forest and Long Short-Term Memory neural network, respectively.
Many autonomous systems forecast aspects of the future in order to aid decision-making. For example, self-driving vehicles and robotic manipulation systems often forecast future object poses by first detecting and tracking objects. However, this detect-then-forecast pipeline is expensive to scale, as pose forecasting algorithms typically require labeled sequences of object poses, which are costly to obtain in 3D space. Can we scale performance without requiring additional labels? We hypothesize yes, and propose inverting the detect-then-forecast pipeline. Instead of detecting, tracking and then forecasting the objects, we propose to first forecast 3D sensor data (e.g., point clouds with $100$k points) and then detect/track objects on the predicted point cloud sequences to obtain future poses, i.e., a forecast-then-detect pipeline. This inversion makes it less expensive to scale pose forecasting, as the sensor data forecasting task requires no labels. Part of this works focus is on the challenging first step -- Sequential Pointcloud Forecasting (SPF), for which we also propose an effective approach, SPFNet. To compare our forecast-then-detect pipeline relative to the detect-then-forecast pipeline, we propose an evaluation procedure and two metrics. Through experiments on a robotic manipulation dataset and two driving datasets, we show that SPFNet is effective for the SPF task, our forecast-then-detect pipeline outperforms the detect-then-forecast approaches to which we compared, and that pose forecasting performance improves with the addition of unlabeled data.
Existing methods of level generation using latent variable models such as VAEs and GANs do so in segments and produce the final level by stitching these separately generated segments together. In this paper, we build on these methods by training VAEs to learn a sequential model of segment generation such that generated segments logically follow from prior segments. By further combining the VAE with a classifier that determines whether to place the generated segment to the top, bottom, left or right of the previous segment, we obtain a pipeline that enables the generation of arbitrarily long levels that progress in any of these four directions and are composed of segments that logically follow one another. In addition to generating more coherent levels of non-fixed length, this method also enables implicit blending of levels from separate games that do not have similar orientation. We demonstrate our approach using levels from Super Mario Bros., Kid Icarus and Mega Man, showing that our method produces levels that are more coherent than previous latent variable-based approaches and are capable of blending levels across games.
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