arXiv subjects

Dilum Fernando

Publications and source records attributed to Dilum Fernando.

4 recordsLinked to original sources

arXiv2026

WASABI: Wasserstein Sampling via Bridge Interpolants

Sampling from Boltzmann distributions is a fundamental problem in physics, chemistry, and biology. We introduce WAsserstein SAmpling via Bridge Interpolants (WASABI), a method that trains a diffusion model to generate samples from a target Boltzmann distribution given access only to the energy function. WASABI minimizes the KL divergence between the distribution generated by its diffusion model and the Boltzmann target using Wasserstein gradient flows. This approach builds on a principle underlying classical sampling methods such as Langevin dynamics. However, applying Wasserstein gradient flows to diffusion models is challenging because the updates require the gradient of the model's own log density, which is generally intractable. We derive a practical training algorithm that avoids computing this gradient. Once trained, WASABI can generate new samples without further evaluations of the energy or its gradient. On alanine dipeptide, WASABI outperforms the best reported baselines using an estimated 3.3 times fewer energy evaluations. It also achieves competitive performance on interacting particle system benchmarks.

stat.ML↗

arXiv2025

I-Diff: Structural Regularization for High-Fidelity Diffusion Models

Denoising Diffusion Probabilistic Models (DDPMs) have significantly advanced generative AI, achieving impressive results in high-quality image and data generation. However, enhancing fidelity without compromising semantic content remains a key challenge in the field. Recent diffusion research in multiple disciplines has introduced objectives and architectural refinements that tighten the match between generated and real data distributions, yielding higher fidelity than earlier generative frameworks. Multi-stage architectures, physics-guided modeling, semantic conditioning, and rarity-aware generation are some of the explored works to achieve this task. However, the integration of structural information of the data distribution into DDPM has largely been unexplored. The conventional DDPM framework relies solely on the $L^2$ norm between the additive and predicted noise to generate new data distributions. We introduce I-Diff, an improved version of DDPM that incorporates a carefully designed regularizer, effectively enabling the model to encode structural information, thereby preserving the inherent fidelity of the data distribution. The proposed approach is validated through extensive experiments on DDPM, Improved DDPM and Latent Diffusion Model across multiple datasets. Empirical results demonstrate significant improvements in fidelity (Density and Precision increase 10% and 37% in CIFAR-100 dataset respectively) across other tested datasets. These results highlight the effectiveness of our method in enhancing the fidelity of the generated data. Notably, improvements across different models highlight the model-agnostic nature of our proposed method in the wider field of generative AI.

cs.LG↗

arXiv2024

Inverse design of programmable shape-morphing kirigami structures

Shape-morphing structures have the capability to transform from one state to another, making them highly valuable in engineering applications. In this study, it is propose a two-stage shape-morphing framework inspired by kirigami structures to design structures that can deploy from a compacted state to a prescribed state under certain mechanical stimuli -- although the framework may also be extended to accommodate various physical fields, such as magnetic, thermal, and electric fields. The framework establishes a connection between the geometry and mechanics of kirigami structures. The proposed approach combines the finite element analysis (FEA), genetic algorithm (GA), and an analytical energy-based model to obtain kirigami designs with robustness and efficiency.

cond-mat.soft↗

arXiv2024

On Micropolar Elastic Foundations

The modelling of heterogeneous and architected materials poses a significant challenge, demanding advanced homogenisation techniques. However, the complexity of this task can be considerably simplified through the application of micropolar elasticity. Conversely, elastic foundation theory is widely employed in fracture mechanics and the analysis of delamination propagation in composite materials. This study aims to amalgamate these two frameworks, enhancing the elastic foundation theory to accommodate materials exhibiting micropolar behaviour. Specifically, we present a novel theory of elastic foundation for micropolar materials, employing stress potentials formulation and a unique normalisation approach. Closed-form solutions are derived for stress and couple stress reactions inherent in such materials, along with the associated restoring stiffness. The validity of the proposed theory is established through verification using the double cantilever beam configuration. Concluding our study, we elucidate the benefits and limitations of the developed theory by quantifying the derived parameters for materials known to exhibit micropolar behaviour. This integration of micropolar elasticity into the elastic foundation theory not only enhances our understanding of material responses but also provides a versatile framework for the analysis of heterogeneous materials in various engineering applications.

cond-mat.soft↗