Differentiate Everything with a Reversible Embeded Domain-Specific Language

Liu, Jinguo; Zhao, Taine

doi:10.48550/arxiv.2003.04617

Cited by 3 publications

(6 citation statements)

References 62 publications

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“…Automatic differentiation is an algorithm implemented through computer programs to compute derivatives of specified functions. Its application in scientific computing has become increasingly widespread [29][30][31][32][33]. There are two forms of automatic differentiation: forward mode and reverse mode.…”

Section: Automatic Differentiationmentioning

confidence: 99%

Discovery of magnesium-aluminum alloys by generative model and automatic differentiation approach

Cheng,

Li,

Zhang

et al. 2024

Modelling Simul. Mater. Sci. Eng.

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Magnesium-aluminum alloy is one of the most common alloy materials in the industry, widely utilized due to its low density and excellent mechanical properties. Investigating the properties or predicting new structures through experimentation inevitably involves complex processes, which consume significant time and resources. To facilitate the discovery, simulations such as Density Functional Theory (DFT) and machine learning (ML) methods are primarily employed. However, DFT incurs significant computational costs. While ML methods are versatile and efficient, they demand high-quality datasets and may exhibit some degree of inaccuracy. To address these challenges, we employ a combination of generative model and automatic differentiation (AD), reducing the search space and accelerating the discovery of target materials. We have predicted a variety of magnesium-aluminum alloys. We conducted structure optimization and property evaluation for ten potentially valuable intermetallic compounds. Ultimately, we identified five stable structures: Mg3Al3, Mg2Al6, Mg4Al12, Mg15Al and Mg14Al2. Among these, Mg4Al12, Mg15Al and Mg14Al2 may hold higher potential for practical applications.

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Section: Automatic Differentiationmentioning

confidence: 99%

Discovery of magnesium-aluminum alloys by generative model and automatic differentiation approach

Cheng,

Li,

Zhang

et al. 2024

Modelling Simul. Mater. Sci. Eng.

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“…The contraction of the tropical tensor network on a GPU shows nice acceleration (>20X) compared to a CPU due to the high arithmetic intensity of the computation. We further compared the performance of finding out the ground state configuration using the forward mode (ForwardDiff.jl [50]) and reverse mode (Nilang.jl [51]) automatic differentia- tion respectively. The reverse mode automatic differentiation is more efficient in this application than the forward model AD which has computational complexity proportional to the number of parameter L 2 .…”

Section: ⊗Lmentioning

confidence: 99%

“…Instead of deriving the backward rule manually, we differentiate the source codes by writing it in a reversible programming manner [51]. Due to the overhead of reversible programming, the memory usage of our reversible implementation is 2L times the original program, while the computational time is also several times slower.…”

Section: Reversible Programming Approach To Compute Gradientsmentioning

confidence: 99%

“…Since the ground state energy is a piecewise linear function of the fields, the numerical finite-difference of the energy with respect to fields suffices to determine the ground state configurations [52]. Alternatively, one can impose an arbitrary order of the spin variables and compute the conditional probability of a variable (b) Wall clock time for computing the ground state configurations using forward (ForwardDiff.jl [50]) on GPU and reverse mode (Nilang.jl [51]) automatic differentiation on CPU respectively.…”

mentioning

confidence: 99%

“…Wall clock time for computing the ground state energy of the (a) Ising spin glass on an open square lattice with L 2 spins. (b) Wall clock time for computing the ground state configurations using forward (ForwardDiff.jl[50]) on GPU and reverse mode (Nilang.jl[51]) automatic differentiation on CPU respectively.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Tropical Tensor Network for Ground States of Spin Glasses

Liu,

Wang,

Zhang

2020

Preprint

Self Cite

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We present a unified exact tensor network approach to compute the ground state energy, identify the optimal configuration, and count the number of solutions for spin glasses. The method is based on tensor networks with the Tropical Algebra defined on the semiring of (R ∪ {−∞}, ⊕, ). Contracting the tropical tensor network gives the ground state energy; differentiating through the tensor network contraction gives the ground state configuration; mixing the tropical algebra and the usual algebra counts the ground state degeneracy. The approach brings together the concepts from graphical models, tensor networks, differentiable programming, and quantum circuit simulation, and easily utilizes computational power of graphical processing units (GPU). For applications, we compute the exact ground state energy of Ising spin glasses with random Gaussian couplings and fields on square lattice up to 1024 spins on a single GPU. Furthermore, we obtain exact ground state energy of ±J Ising spin glass on the chimera graph of D-Wave quantum annealer of 512 qubits in less than 100 seconds. Lastly, we investigate the exact value of the residual entropy of ±J spin glasses on the chimera graph which has not been reported before.

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Automatic differentiation and its applications in physics simulation

Liu¹,

Xu²

2021

Acta Phys. Sin.

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Automatic differentiation is a technology to differentiate a computer program automatically. It is known to many people for its use in machine learning in recent decades. Nowadays, researchers are becoming increasingly aware of its importance in scientific computing, especially in the physics simulation. Differentiating physics simulation can help us solve many important issues in chaos theory, electromagnetism, seismic and oceanographic. Meanwhile, it is also challenging because these applications often require a lot of computing time and space. This paper will review several automatic differentiation strategies for physics simulation, and compare their pros and cons. These methods include adjoint state methods, forward mode automatic differentiation, reverse mode automatic differentiation, and reversible programming automatic differentiation.

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Differentiate Everything with a Reversible Embeded Domain-Specific Language

Cited by 3 publications

References 62 publications

Discovery of magnesium-aluminum alloys by generative model and automatic differentiation approach

Discovery of magnesium-aluminum alloys by generative model and automatic differentiation approach

Tropical Tensor Network for Ground States of Spin Glasses

Automatic differentiation and its applications in physics simulation

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