For example, electricity consumption shows specific temporal variations spanning seasonal, daily and hourly granularities. Figure 1, illustrates a time series of a stock over one year, in which relations between patches of different scales are critical to capture more information regarding the local and global temporal dependencies from various perspectives. programmer This calls for multi-scale modeling of time series9 and representation of inter series correlations10. Can theory-driven machine learning approaches uncover meaningful and compact representations for complex inter-connected processes, and, subsequently, enable the cost-effective exploration of vast combinatorial spaces?
- Artificial intelligence through deep learning is an exciting recent development that has seen remarkable success in solving problems, which are difficult for humans.
- In addition to memory, the 32-bit limitation of current GPU systems is particularly troubling for modeling biological systems where steep gradients and very fast multirate dynamics may require 64-bit arithmetic, which, in turn, may require ten times more computational time with the current technologies.
- Another limitation of the current research is the single step decoding of the encoded representation, particularly in dealing with long horizon prediction, which raises the risk of overfitting and makes the model more susceptible to be affected by noise.
- The concept of multiscale modelling has emerged over the last few decades to describe procedures that seek to simulate continuum-scale behaviour using information gleaned from computational models of finer scales in the system, rather than resorting to empirical constitutive models.
Computational Modeling
A major challenge in the biological, biomedical, and behavioral sciences is to understand systems for which the underlying data are incomplete and the physics are not yet fully understood. In other words, with a complete set of high-resolution data, we could apply machine learning to explore design spaces and identify correlations; with a validated and calibrated set of physics equations and material parameters, we could apply multiscale modeling to predict system dynamics and identify causality. By Multi-scale analysis integrating machine learning and multiscale modeling we can leverage the potential of both, with the ultimate goal of providing quantitative predictive insight into biological systems. Figure 2 illustrates how we could integrate machine learning and multiscale modeling to better understand the cardiac system.
Model efficiency
Our multi-step decoder, improves the prediction error in most cases, specifically when the forecast horizon is long, e.g. 720. For example, in traffic forecasting, consisting of 862 variables across 720 future timestamps, the utilization of a multi-step decoder yields an MAE error reduction of 1%. We utilize a different kernel size for each dataset in the channel summarization part of the channel-wise attention in order to project the key and values, depending on the performance improvement.
- Can we eventually utilize our models to identify relevant biological features and explore their interaction in real time?
- Several works have leveraged Graph Neural Networks (GNN) for time series forecasting, specifically for traffic forecasting.
- Prediction results of our model applied to the Traffic dataset with different forecasting horizons.
- A sketch of the historical developments in the field of numerical analysis that has laid the foundations for much of scientific computing is provided in Table 2.
- In current terms, HPC broadly involves the use of new architectures (such as graphical processing unit GPU computing), computing in distributed systems, cloud‐based computing, and computing in parallel to massively parallel platforms or extreme hardware architectures for running computational models (Figure 2).
- However, at the nanoscopic to mesoscopic length scales, neither the molecular description using MD nor a continuum description based on the Navier–Stokes equation are optimal to study nanofluid flows.
Motivation for multiple-scale analysis
Over the past two decades, multiscale modeling has emerged into a promising tool to build individual organ models by systematically integrating knowledge from the tissue, cellular, and molecular levels, in part fueled by initiatives like the United States Federal Interagency Modeling and Analysis Group IMAG5. Depending on the scale of interest, multiscale modeling approaches fall into two categories, ordinary differential equation-based and partial differential equation-based approaches. Within both coding jobs categories, we can distinguish data-driven and theory-driven machine learning approaches. Unfortunately, ill-posed problems are relatively common in the biological, biomedical, and behavioral sciences and can result from inverse modeling, for example, when identifying parameter values or identifying system dynamics.
- BC thanks Alireza Yasdani for stimulating discussions on the amplification scale bridging techniques.
- This indicates that Transformer models are still powerful in forecasting long-term time series tasks.
- The subscript αil labels the ith atom of type α in the lth sampled atomic configuration.
- Recent trends suggest that integrating machine learning and multiscale modeling could become key to better understand biological, biomedical, and behavioral systems.