Transient growth analysis has been extensively studied in asymptotically stable flows to identify their short-term amplification of perturbations. Generally, in global transient growth analyses, matrix-free methods are adopted, requiring the construction of adjoint equations, either in the discrete or continuous form. This paper introduces a data-driven algorithm that circumvents the adjoint equations by extracting the optimal initial perturbation and its energy growth over a specified time horizon from transient snapshots of perturbations. This method is validated using data from the linearised complex Ginzburg-Landau equation, backward-facing step flow, and the Batchelor vortex. Unlike model-based methods, which require $S$ sets of integrations of the linearised governing equation and its adjoint for $S$ time horizons, the proposed approach collects the snapshots of $S$ time horizons in one integration of the linearised equation. Furthermore, this study provides a robust framework for utilising proper orthogonal decomposition (POD) modes to synthesise optimal modes. The developed capacity to conduct transient growth analyses without solving the adjoint equations is expected to significantly reduce the barriers to transient dynamics research.

The discovery and optimization of high-energy materials (HEMs) are constrained by the prohibitive computational expense and prolonged development cycles inherent in conventional approaches. In this work, we develop a general neural network potential (NNP) that efficiently predicts the structural, mechanical, and decomposition properties of HEMs composed of C, H, N, and O. Our framework leverages pre-trained NNP models, fine-tuned using transfer learning on energy and force data derived from density functional theory (DFT) calculations. This strategy enables rapid adaptation across 20 different HEM systems while maintaining DFT-level accuracy, significantly reducing computational costs. A key aspect of this work is the ability of NNP model to capture the chemical activity space of HEMs, accurately describe the key atomic interactions and reaction mechanisms during thermal decomposition. The general NNP model has been applied in molecular dynamics (MD) simulations and validated with experimental data for various HEM structures. Results show that the NNP model accurately predicts the structural, mechanical, and decomposition properties of HEMs by effectively describing their chemical activity space. Compared to traditional force fields, it offers superior DFT-level accuracy and generalization across both microscopic and macroscopic properties, reducing the computational and experimental costs. This work provides an efficient strategy for the design and development of HEMs and proposes a promising framework for integrating DFT, machine learning, and experimental methods in materials research. (To facilitate further research and practical applications, we open-source our NNP model on GitHub: this https URL.)