# Inverse Reconstruction of Shock Time Series from Shock Response Spectrum Curves using Machine Learning

arXiv: https://arxiv.org/abs/2603.03229 · HTML: https://mlsanity.com/paper/2603.03229/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 22 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Hybrid Spectrogram and Waveform Source Separation](https://mlsanity.com/paper/2111.03600/) (2021)
- [TorchAudio 2.1: Advancing speech recognition, self-supervised learning, and audio processing components for PyTorch](https://mlsanity.com/paper/2310.17864/) (2023)
- [Differentiable All-pole Filters for Time-varying Audio Systems](https://mlsanity.com/paper/2404.07970/) (2024)
- [MinGRU-Based Encoder for Turbo Autoencoder Frameworks](https://mlsanity.com/paper/2503.08451/) (2025)

## Built on by (most cited first, 1 of 1)

- [Inverse Synthesis of Shock Time Series from Shock Response Spectra Using Ensembles of Conditional Variational Autoencoders](https://mlsanity.com/paper/2610.12820/) (2026)

## Abstract (arXiv)

The shock response spectrum (SRS) is widely used to characterize the response of single-degree-of-freedom (SDOF) systems to transient accelerations. Because the mapping from acceleration time history to SRS is nonlinear and many-to-one, reconstructing time-domain signals from a target spectrum is inherently ill-posed. Conventional approaches address this problem through iterative optimization, typically representing signals as sums of exponentially decayed sinusoids, but these methods are computationally expensive and constrained by predefined basis functions. We propose a conditional variational autoencoder (CVAE) that learns a data-driven inverse mapping from SRS to acceleration time series. Once trained, the model generates signals consistent with prescribed target spectra without requiring iterative optimization. Experiments demonstrate improved spectral fidelity relative to classical techniques, strong generalization to unseen spectra, and inference speeds three to six orders of magnitude faster. These results establish deep generative modeling as a scalable and efficient approach for inverse SRS reconstruction.