Deep Learning Applied to Computational Mechanics:A Comprehensive Review,State of the Art,and the Classics

Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.

RELIABILITY ANALYSIS FOR AN AERO ENGINE TURBINE DISK UNDER LOW CYCLE FATIGUE CONDITION

Reliability analysis methods based on the linear damage accumulation law (LDAL) and load-life interference model are studied in this paper. According to the equal probability rule, the equivalent loads are derived, and the reliability analysis method based on load-life interference model and recurrence formula is constructed. In conjunction with finite element analysis (FEA) program, the reliability of an aero engine turbine disk under low cycle fatigue (LCF) condition has been analyzed. The results show the turbine disk is safety and the above reliability analysis methods are feasible.

ABSOLUTE MONOTONICITY INVOLVING THE COMPLETE ELLIPTIC INTEGRALS OF THE FIRST KIND WITH APPLICATIONS

Let K(r)be the complete elliptic integrals of the first kind for r∈(0,1)and f_(p)(x)=[(1−x)^(p)K(√x)].Using the recurrence method,we find the necessary and sufficient conditions for the functions−f′_(p),ln f_(p),−(ln f_(p))^((i))(i=1,2,3)to be absolutely monotonic on(0,1).As applications,we establish some new bounds for the ratios and the product of two complete integrals of the first kind,including the double inequalities exp[r^(2)(1−r^(2))/^(64)]/(1+r)^(1/4)<K(r)/K(√r)<exp[−r(1−r)/4],π/2 exp[θ0(1−2r^(2))]<π/2 K(r′)/K(r)<π/2(r′/r)^(p)exp[θ_(p)(1−2r^(2))],K^(2)(1/√2)≤K(r)K(r′)≤1/√2rr′K^(2)(1/√2)for r∈2(0,1)and p≥13/32,where r′=√1−r^(2) and θ_(p)=2Γ(3/4)^(4)/π^(2)−p.

INTRAVESICAL INSTILLATION OF INTERLEUKIN-2 AN EFFECTIVE METHOD FOR PREVENTING THE RECURRENCE OF BLADDER CANCER

The result of intravesical instillation with interleukin-2 (IL-2) for preventing the recurrence of bladder cancer and discussion of its mechanism was reported. 20 patients with histologically confirmed bladder transitional cell carcinoma were investigated. 2 000 u IL 2 was intravesically instillated every day for six days after resection of the neoplasm. The serum level of tumor necrosis factor (TNF) was significantly increased in 17 patients after IL-2 therapy. Recurrence occurred in 4 patients during the follow-up period of 10-18 months. The basic level of serum TNF was low and was not increased or even decreased after IL-2 in these patients. On the contrary, recurrence did not occur in another 5 patients with low basic level of TNF, but it was significantly increased after treatment of IL-2. TNF played a key role in preventing the recurrence of bladder cancer. The patients who had low basic level of TNF, which did not markedly increase or even decrease after IL-2 therapy were at high risk of recurrenc

The dynamics of one-dimensional random quantum XY system with Dzyaloshinskii-Moriya interaction

In this paper,the effects of random variables on the dynamics of the s = 1/2 XY model with the Dzyaloshinskii-Moriya interaction are studied.By means of the recurrence relation method in the high-temperature limit,we calculate the spin autocorrelation functions as well as the corresponding spectral densities for the cases that the exchange couplings between spins or external magnetic fields satisfy the double-Gaussian distribution.It is found that when the standard deviation of random exchange coupling δJ（or the standard deviation of random external field δB） is small,the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one.However,when δJ（or δB） is large,the crossover vanishes,and the system shows a central-peak behavior or the most disordered one.We also analyze the cases in which the exchange couplings or the external fields satisfy the bimodal and the Gaussian distributions.Our results show that for all the cases considered,the dynamics of the above system is similar to that of the one-dimensional random XY model.