There has been much progress in ab initio nuclear many-body theory in recent years, including a first attempt on an ab initio based mass table and a calculation of the neutron skin of $^{208}$Pb based on two- plus three-nucleon interactions from chiral Effective Field Theory, with a sophisticated statistical uncertainty quantification. Going forward, there is a need to continue extending the capabilities of ab initio nuclear many-body theory to observables in medium-mass and heavy open-shell nuclei, enhance the description of exotic nuclei, and to build on theoretical and computational advances in nuclear structure to tackle nuclear dynamics. These advances in ab initio nuclear many-body theory, along with new methods for carrying controlled uncertainties into the relevant calculations, will provide new insight into nuclear forces and phenomena, as well as important input for searches for Beyond-Standard Model physics or nuclear astrophysics. All of these goals requires theoretical and computational improvements of current nuclear many-body methods in order to enhance the stability of predictions, determine proper theoretical error bars, and to provide greater computational efficiency. In this body of work, we pursue these directions for the In-Medium Similarity Renormalization Group (IMSRG), which has become an important tool in ab initio nuclear many-body theory over the past decade.We will discuss three major contributions in these directions. First, we present a model for the future infrastructure of IMSRG production codes using tensor network architectures, and show that it can soften the memory requirements and favorably improve the efficiency of IMSRG calculations. Second, we present a methodological improvement, the so-called reference state ensemble, that allows us to mitigate truncation errors in the IMSRG flow without performing calculations at a higher truncation rank. We show that the reference state ensemble improves the stability and accuracy of the IMSRG flow by "informing'' the underlying operator basis about the features of the many-body system's excitations. Last but not least, we use a data-driven technique called Dynamic Mode Decomposition (DMD) for emulating the IMSRG solution which reduces the cost of complete integration to convergence from hundreds or thousands of iterations to only tens of iterations. We also present a parametric emulation technique, powered by DMD and trained on IMSRG data, which we show can robustly predict the IMSRG results for Hamiltonians, including chiral two- plus three-nucleon Hamiltonians with more than 20 parameters. We show that the parametric emulator can produce a global sensitivity analysis of statistical significance in only a few minutes, where full IMSRG(2) calculations would take thousands of years---improving the feasibility of uncertainty quantification for the IMSRG.
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