arXiv subjects

Jian-Nan Chen

Publications and source records attributed to Jian-Nan Chen.

7 recordsLinked to original sources

arXiv2025

On the uncertainty principle of neural networks

In this study, we explore the inherent trade-off between accuracy and robustness in neural networks, drawing an analogy to the uncertainty principle in quantum mechanics. We propose that neural networks are subject to an uncertainty relation, which manifests as a fundamental limitation in their ability to simultaneously achieve high accuracy and robustness against adversarial attacks. Through mathematical proofs and empirical evidence, we demonstrate that this trade-off is a natural consequence of the sharp boundaries formed between different class concepts during training. Our findings reveal that the complementarity principle, a cornerstone of quantum physics, applies to neural networks, imposing fundamental limits on their capabilities in simultaneous learning of conjugate features. Meanwhile, our work suggests that achieving human-level intelligence through a single network architecture or massive datasets alone may be inherently limited. Our work provides new insights into the theoretical foundations of neural network vulnerability and opens up avenues for designing more robust neural network architectures.

cs.LG↗

arXiv2024

Is AI Robust Enough for Scientific Research?

We uncover a phenomenon largely overlooked by the scientific community utilizing AI: neural networks exhibit high susceptibility to minute perturbations, resulting in significant deviations in their outputs. Through an analysis of five diverse application areas -- weather forecasting, chemical energy and force calculations, fluid dynamics, quantum chromodynamics, and wireless communication -- we demonstrate that this vulnerability is a broad and general characteristic of AI systems. This revelation exposes a hidden risk in relying on neural networks for essential scientific computations, calling further studies on their reliability and security.

cs.LG↗

arXiv2024

Symmetry Breaking in Neural Network Optimization: Insights from Input Dimension Expansion

Understanding the mechanisms behind neural network optimization is crucial for improving network design and performance. While various optimization techniques have been developed, a comprehensive understanding of the underlying principles that govern these techniques remains elusive. Specifically, the role of symmetry breaking, a fundamental concept in physics, has not been fully explored in neural network optimization. This gap in knowledge limits our ability to design networks that are both efficient and effective. Here, we propose the symmetry breaking hypothesis to elucidate the significance of symmetry breaking in enhancing neural network optimization. We demonstrate that a simple input expansion can significantly improve network performance across various tasks, and we show that this improvement can be attributed to the underlying symmetry breaking mechanism. We further develop a metric to quantify the degree of symmetry breaking in neural networks, providing a practical approach to evaluate and guide network design. Our findings confirm that symmetry breaking is a fundamental principle that underpins various optimization techniques, including dropout, batch normalization, and equivariance. By quantifying the degree of symmetry breaking, our work offers a practical technique for performance enhancement and a metric to guide network design without the need for complete datasets and extensive training processes.

cs.LG↗

arXiv2023

Leveraging Neural Networks with Attention Mechanism for High-Order Accuracy in Charge Density in Particle-in-Cell Simulation

In this research, we introduce an innovative three-network architecture that comprises an encoder-decoder framework with an attention mechanism. The architecture comprises a 1st-order-pre-trainer, a 2nd-order-improver, and a discriminator network, designed to boost the order accuracy of charge density in Particle-In-Cell (PIC) simulations. We acquire our training data from our self-developed 3-D PIC code, JefiPIC. The training procedure starts with the 1st-order-pre-trainer, which is trained on a large dataset to predict charge densities based on the provided article positions. Subsequently, we fine-tune the 1st-order-pre-trainer, whose predictions then serve as inputs to the 2nd-order-improver. Meanwhile, we train the 2nd-order-improver and discriminator network using a smaller volume of 2nd-order data, thereby achieving to generate charge density with 2nd-order accuracy. In the concluding phase, we replace JefiPIC's conventional particle interpolation process with our trained neural network. Our results demonstrate that the neural network-enhanced PIC simulation can effectively simulate plasmas with 2 nd-order accuracy. This highlights the advantage of our proposed neural network: it can achieve higher-accuracy data with fewer real labels.

physics.comp-ph↗

arXiv2022

Charge-dependent directed flows in heavy-ion collisions by Boltzmann-Maxwell equations

We have calculated the directed flow $v_{1}$ and charge-dependent directed flow $Δv_{1}$ for pions and protons in Au+Au collisions at $\sqrt{s_{NN}}=200$GeV by solving the coupled Boltzmann-Maxwell equations self-consistently. Our numerical results show that $v_{1}$ for pions and protons are all negative in the positive mid rapidity region and have similar behavior and magnitude. In contrast we find a quite different behavior in $Δv_{1}$ for pions and protons. The difference lies in that $Δv_{1}$ for protons mainly comes from pressure gradients of the medium, while the dominant contribution to $Δv_{1}$ for pions is from electromagnetic fields. Our results indicate that the effect of the electric field will slightly exceed that of the magnetic and lead to a small negative slope of $Δv_{1}$ for pions

hep-ph↗

arXiv2021

JefiGPU: Jefimenko's Equations on GPU

We have implemented a GPU version of the Jefimenko's equations -- JefiGPU. Given the proper distributions of the source terms $ρ$ (charge density) and $\mathbf{J}$ (current density) in the source volume, the algorithm gives the electromagnetic fields in the observational region (not necessarily overlaps the vicinity of the sources). To verify the accuracy of the GPU implementation, we have compared the obtained results with that of the theoretical ones. Our results show that the deviations of the GPU results from the theoretical ones are around 5\%. Meanwhile, we have also compared the performance of the GPU implementation with a CPU version. The simulation results indicate that the GPU code is significantly faster than the CPU version. Finally, we have studied the parameter dependence of the execution time and memory consumption on one NVIDIA Tesla V100 card. Our code can be consistently coupled to RBG (Relativistic Boltzmann equations on GPUs) and many other GPU-based algorithms in physics.

physics.comp-ph↗

arXiv2021

Two typical collective behaviors of the heavy ions expanding in cold plasma with ambient magnetic field

We have numerically studied the evolution of the heavy ions that expand in a cold background plasma at a large scale. Two typical collective behaviors of the heavy ions are identified with the conditions where only the traversing heavy ion's initial total mass is different. Our work has demonstrated that a difference in the initial total mass of the moving heavy ions is able to induce completely different collective behaviors of the plasma. The simulation is performed via the hybrid model, in which the ions and electrons are treated as classical particles and mass-less fluid, respectively. Due to the imbalance of the electric and magnetic force on the heavy ions, these particles will evolve into different collective patterns at the later time. These patterns manifest a rather different stopping behavior of the moving ions and an opposite drifting direction of the electron fluid at the rim of the expanding plasma. Further numerical and analytical calculations show that the imbalance depends not only on the number densities of the plasma ions, but also on the spatial variations of the magnetic fields. Our work reveals that the collective behavior of the heavy ions is highly non-linear, and the non-linearity is able to induce different phenomena in the evolution of the system at a large scale.

physics.plasm-ph↗