Heterogeneous memory systems that combine high-bandwidth memory (HBM) with commodity DRAM can accelerate bandwidth-bound HPC workloads, but current page placement largely depends on manual tuning or OS heuristics not designed for multi-tier dynamics. We present SHAMBLES, a kernel-integrated framework that profiles application memory behavior at low overhead and migrates data across tiers without requiring application changes. SHAMBLES exposes a policy-agnostic interface and a lightweight user-space runtime with pluggable policies (e.g. recency and frequency based) as well as static placement for controlled studies. A logging mode provides reproducible timelines of allocations and migrations to aid analysis. We implement SHAMBLES on a commodity Linux system with HBM and DDR exposed as NUMA nodes and evaluate it with the HPCG, DGEMM benchmarks and Himeno stencil mini-app. Our design and methodology show how transparent, policy-driven migration can respond to changing access locality and concentrate hot data in HBM without developer intervention, offering a practical path to performance portability on tiered memory. Results from HPCG show that we can maintain up to 93.75% of the all-in-HBM baseline performance, while keeping only 40% of the problem size in the HBM. DGEMM experiments show that dynamic policies in SHAMBLES sustain up to 99% of the all-in-HBM performance, while keeping only one third of the DGEMM matrix footprint in HBM. For Himeno, SHAMBLES shows that fast-tier selection must be both workload-aware and size-aware: with a 50% fast-tier budget, it can outperform fixed all-in-HBM and all-in-DDR placements for the L size, while the XL size shifts back toward HBM.

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