Transformer Encoder-Decoder for Multi-Dimensional Differential Equations
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods are limited to modeling one-dimensional Ordinary Differential Equations (ODEs) or simple equations, failing to effectively handle multi-dimensional time series data.
Innovation Solution
A modified Large Language Model (LLM) architecture with an encoder-decoder system that iteratively constructs differential equations by translating multi-dimensional time series into symbolic form, using a signal embedding and equation embedding process, and applying transformer networks for efficient learning.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If existing methods are used to model differential equations, then one-dimensional ODEs or simple equations can be handled, but multi-dimensional time series data cannot be effectively modeled
Solution Approach 1:
The patent applies universality by designing a unified transformer-based architecture that can handle both one-dimensional and multi-dimensional time series data. The model uses a generic encoder-decoder structure with configurable input dimensions, allowing it to universally process different types of differential equations (ODEs, PDEs) and varying data dimensions through the same fundamental mechanism, thereby achieving multi-functionality without requiring separate specialized models for each case.
Solution Approach 2:
The patent implements dimensionality change by extending the input representation from scalar sequences to multi-dimensional tensors. The encoder processes N-dimensional time series data by incorporating spatial dimension embeddings alongside temporal sequences, transforming the input structure to accommodate multi-dimensional data while maintaining the transformer architecture's core attention mechanisms. This allows the model to capture both temporal dynamics and spatial relationships in the data.
2Productivity
If a modified LLM architecture is introduced to enable efficient learning of multi-dimensional differential equations, then modeling capability is improved, but system complexity increases
Solution Approach 1:
The patent applies segmentation by dividing the model into distinct functional modules: an encoder that processes input time series data, a decoder that generates differential equation symbols, and intermediate embedding layers that transform data representations. This modular segmentation allows each component to be optimized independently for its specific task, improving overall learning efficiency while making the complex architecture more manageable and trainable through targeted loss functions and gradient flow control.
Solution Approach 2:
The patent introduces intermediary embedding layers that act as mediators between the input multi-dimensional time series and the output differential equation symbols. These embedding layers transform the raw input data into a latent representation space that the transformer architecture can effectively process, serving as a bridge that facilitates efficient learning by aligning the data representation with the model's internal processing mechanisms and reducing the complexity of direct mapping.
Data Source
Figure 1
Figure 2
Figure 3
AI summary
A method of iteratively constructing a differential equation for an input time series measured on a technical system using a machine learning system (1) comprising an encoder (11) and a decoder (12), said method comprising: Propagating (S14) the input time series through the encoder to obtain a signal encoding of said input time series. Generating an initial shared equation embedding plus signal encoding from the signal encoding, wherein the initial shared equation embedding plus signal encoding equals the signal encoding. Iteratively applying (S15) the decoder on the shared equation embedding plus signal encoding to iteratively outputting individual terms of the differential equation and aggregate the individual terms to the differential equation, wherein after each outputted term by the decoder, the shared equation embedding plus signal encoding is updated by concatenating the signal encoding with an updated equation embedding for the current aggregated differential equation.